TEL AVIV UNIVERSITY - UCSB MRSEC › ~roy › ThesisBeck.pdfﬁelds” by Roy Beck-Barkai in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy. Dated:

TEL AVIV UNIVERSITY a aia`-lz zhiqxaipe`TUNNELING INTO HIGH TC SUPERCONDUCTOR THIN

FILMS IN THE PRESENCE OF HIGH MAGNETIC

FIELDS

By

Roy Beck-Barkai

SUBMITTED IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

AT

TEL-AVIV UNIVERSITY, SCHOOL OF PHYSICS AND ASTRONOMY

TEL-AVIV, ISRAEL

APRIL 2006

c© Copyright by Roy Beck-Barkai, 2006

TEL-AVIV UNIVERSITY, SCHOOL OF PHYSICS AND

ASTRONOMY

DEPARTMENT OF

CONDENSED MATTER

The undersigned hereby certify that they have read and recommend

to the Faculty of Raymond and Beverly Sackler Faculty of Exact

Sciences for acceptance a thesis entitled “Tunneling into High Tc

superconductor thin films in the presence of high magnetic

fields” by Roy Beck-Barkai in partial fulfillment of the requirements

for the degree of Doctor of Philosophy.

Dated: April 2006

External Examiner:

Research Supervisor:Prof. Guy Deutscher

Examing Committee:

ii

To the one I love most.

iv

Table of Contents

Table of Contents v

Acknowledgements ix

Abstract xi

1 Introduction 1

2 Theoretical background 32.1 High Tc superconductivity . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Order parameter and d -wave superconductors . . . . . . . . . . . . . 42.3 ASJ reflections and bound states . . . . . . . . . . . . . . . . . . . . 62.4 Tunneling experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5 Splitting of the Zero Bias Conductance Peak . . . . . . . . . . . . . . 22

2.5.1 Doppler shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5.2 Induced node removal . . . . . . . . . . . . . . . . . . . . . . 27

3 Experimental setup 313.1 Thin film deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2 Tunneling junction formation and measurement . . . . . . . . . . . . 333.3 Film characterizations . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.1 Resistivity measurements . . . . . . . . . . . . . . . . . . . . . 363.3.2 Microscopy and spectroscopy measurements . . . . . . . . . . 37

4 Origin of hysteresis in magnetic field ZBCP splitting 41

5 Order parameter node-removal in magnetic fields 49

6 Determination of the critical current by nodal tunnelling 55

7 Transition in the tunneling conductance in high magnetic fields 59

8 Supplementary results 678.1 Non-concomitance in spontaneous and induced ZBCP splitting . . . . 688.2 On the origin of spontaneous splitting . . . . . . . . . . . . . . . . . . 728.3 The effect of doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

v

9 Summary and conclusions 83

vi

vii

This work was carried out under the supervision of Professor Guy Deutscher

viii

Acknowledgements

My deepest and most humble gratitude is given to professor Guy Deutscher, my

supervisor, for his constant support and guidance during my research. Among many

things, I shall cherish the long and fruitful discussions, usually over coffee, in which

I had the pleasure to lay in the shadow of a humble man and a great physicist. I am

most thankful for the great pleasure and enjoyment I had working in his laboratory.

I am grateful to Dr. Yoram Dagan, my second mentor, who taught me most of

the experimental techniques I used during this work. I thank Guy Leibovitch, for

the constant collaboration in each and every experiment I conducted. I would like

to thank him for the many enjoyable hours spent shearing his thoughts, ideas and

results. Special thanks goes to Dr. Amir Kohen for the great fruitful talks and ideas

we shared, for teaching me theory and correcting my English.

I would like also to thank:

Professor Roman Mints for the many hours spent together trying to understand

the theoretical aspects of my work. Professor Oded Millo, Professor Gad Koren and

Dr. Amos Sharoni for the collaborations and discussions over the years.

Professor Alexander Gerber and Dr. Alexander Milner for their collaboration in

the high magnetic fields experiments. Professor Richard Green and his staff for the

enriching visit at the Center for Superconductivity - University of Maryland. Not

ix

x

forgetting Yoram, Dovrat, Chen and Tamar who made my stay very enjoyable.

Mishael Azouly and Olivier Cohen for their most professional technical support

and brilliant ideas. I thank Avner Yehezkel from the School of Physics workshop for

his superb ideas and implementations.

I acknowledge the support from the Heinrich Herz-Minerva Center for High Tem-

perature Superconductivity, the Israel Science Foundation, the Oren Family Chair of

Experimental Solid State Physics and Tom and Rae Mandel Special Fellowships for

Advanced Degrees, Australia. Part of this work was conducted with the assistance of

the Fulbright scholarship.

I would also like to thank the many colleagues and friends I enjoyed working with:

Dr. Hector Castro, Boaz Almog, Gal Elhalel, Shay Hacohen and Dr. Eli Farber.

My friends across the corridor: Moshe Shkol, Hezi Amiel, Maayan Moshe and Itay

Sternfeld. A special thank-you goes to my dearest friend Ronen Ingbir who is to

blame for my career choice.

I am grateful to my parents and sister for their patience and love. Without them

this work would never have come into existence (literally).

Finally, my greatest gratitude goes to the one and only, my love, my best friend

and wife - Sarit - for the intense love, support and understanding. You are my

inspiration and muse.

Abstract

We measured the tunneling conductance of a YBa2Cu3O7−x high Tc superconductor

in the presence of high magnetic fields. Using planar indium junctions, we studied

the superconductor density of states and the order-parameter symmetry.

Typical planar tunneling conductance into the CuO2 planes exhibits two main

characteristics: a Zero-Bias Conductance Peak (ZBCP) and a gap-like feature (GLF).

The first is a distinct mark for the d -wave order-parameter symmetry, while the later

marks the maximum superconducting gap energy scale. In this work we studied the

evolution of both the ZBCP and GLF in the presence of high magnetic fields.

The ZBCP splits into two peaks under applied magnetic fields perpendicular to

the CuO2 planes. We show that, while keeping the magnetic field parallel to the film

surface, the ZBCP splitting is remarkably different for films with different crystallo-

graphic orientations. We discuss the different mechanisms responsible for the ZBCP

splitting. In (110) oriented films, we find that the main origin for the ZBCP splitting

in high magnetic fields, in particular in decreasing fields, is due to a node-removal

mechanism.

xi

xii

In addition, we discuss and explain the ZBCP splitting hysteresis in magnetic

fields. We show that, in increasing magnetic fields, the bound states are Doppler

shifted by the screening currents, and hence produce a larger ZBCP splitting than

in decreasing fields where the screening current is dramatically reduced due to the

absence of surface barriers.

Furthermore, we show that tunneling spectra on the superconducting energy gap

scale is discontinuously modified in high magnetic fields. We discuss this effect in

terms of a first order phase transition, possibly induced by currents, to a more fully

gapped order-parameter symmetry.

Last, we discuss the effect of doping on the tunneling spectra at high magnetic

fields. We notice that, in high enough fields, the ZBCP splitting follows a universal

behavior, proportional to the square-root of the applied magnetic field. We discuss

possible origins for this universal behavior and speculate that low-field data suggests

a modification in the order-parameter symmetry occurring at and beyond optimum

doping.

Chapter 1

Introduction

The era of high temperature superconductivity began two decades ago with the dis-

covery of a new superconducting compound (Ba-La-Cu-O) by Bednorz and Muller

in 1986. [1] While the new compound’s critical temperature (Tc) was not noticeably

higher then those previously reported, it was noticed that similar compounds, also

having copper oxide planes, have much higher Tc values. Moreover, this group of

compounds, later known as the high Tc Cuprate family, seemed not to obey the same

physical mechanism that explained low Tc superconductivity. To date, the mechanism

responsible for high Tc superconductivity is still under intense debate.

Tunneling measurements became one of the most important probes of supercon-

ductivity, since the early work of Ivar Giaever.[2] Tunneling measurements advantage

is the ability to measure, from the differential conductance, the superconductor elec-

tronic density of states. Therefore, it allows us to study the electronic structure of

excitations and the superconductor gap under various conditions such as temperature,

1

2 Introduction

magnetic field and applied current. Giaever’s measurements of the density of states

in low Tc superconductors provided strong experimental support to the Bardeen,

Schrieffer and Copper theory known as the BCS theory of superconductivity.[3]

In this work, we study the effect of strong magnetic fields on the high Tc super-

conductor YBa2Cu3O7−x via planar tunneling junction measurements. This work is

a summary of five published peer-reviewed papers and additional measurements soon

to be published.

We begin with the theoretical background of tunneling into high Tc supercon-

ductors and the effect of magnetic fields in chapter 2. Next, we present our sample

preparation technique, experimental setup and films’ characterization in chapter 3.

In chapter 4 we present our studies on the magnetic field hysteresis of the zero bias

conductance peak splitting. Experimental evidence of order-parameter node-removal

in the presence of magnetic fields are presented in chapter 5. The applicability of the

preceding result is demonstrated in chapter 6 where a non-destructive critical current

measurement technique is suggested.

Chapter 7 is devoted to studies focusing on the gap’s energy scale. These mea-

surements, show a transition in the tunneling density of states, in high magnetic

fields. Chapter 8 presents new, still unpublished, results, of our study of the effect

of different oxygen doping levels on the tunneling density of states in high magnetic

fields. The summary and conclusions are presented last in chapter 9.

Chapter 2

Theoretical background

In this chapter, we summarize the theoretical background relevant to tunneling mea-

surements. We begin with a general introduction to high Tc superconductivity (HTS).

Next, we explain the theoretical tunneling calculation, first in the case of isotropic

low Tc superconductors (LTS), known as Blonder, Tinkham and Kalpwijk model, and

then the extension made by Tanaka and Kashiwaya for the case of d -wave HTS. We

end this chapter with a discussion on several theoretical predictions and mechanisms

regarding the effect of an applied magnetic field on the tunneling conductance.

2.1 High Tc superconductivity

The basic difference between LTS and HTS is the quasi two-dimensionality of su-

perconductivity, believed to take place in the CuO2 layers of the latter. Unlike the

phonon-mediated electron-electron interaction, acknowledged to be responsible for

superconductivity in LTS, the case of HTS seems to be more complicated. Thus far,

3

4 Theoretical background

the Bardeen, Cooper and Schrieffer theory, known as the BCS theory,[3] which fully

explains LTS, has failed to explain many experimental results of HTS.

Among the many differences between LTS and HTS cuprates, it has been found

that the order-parameter in the latter has an anisotropic nature, i.e. the order-

parameter has a different amplitude and phase along different directions in momentum

space. This is in contrast to the isotropic order-parameter symmetry in LTS.

However, basic properties of the LTS superconducting state hold for HTS; zero

dc resistance (up to a certain critical current - jc) and diamagnetic properties, as

in strong type II superconductors (up to a certain critical field Hc2). The fact that

these critical values, as well as Tc, are much higher in HTS, led many to believe that

HTS-based devices, hopefully working at room temperature or with comparatively

cheap cooling systems, will soon be embedded where normal conducting materials

are currently used.

2.2 Order parameter and d-wave superconductors

As previously mentioned, the symmetry of the order-parameter in the high Tc cuprates

superconductors is anisotropic. Many experimental results led physicists to conclude

that the symmetry of the order-parameter is dx2−y2 . This symmetry is shown in Fig.

2.1 where the order-parameter amplitude is plotted as a function of the momentum

direction. The d -wave symmetry reflects the electronic properties in the CuO2 planes

2.2. Order parameter and d-wave superconductors 5

of the cuprates.[4] The d -wave symmetry of the superconducting gap, ∆(r), restricts

possible theoretical mechanisms responsible for high Tc superconductivity to those

which do produce that symmetry. This has had a great impact on theories trying to

explain HTS. The d -wave symmetry order-parameter can be written as:

∆(k) = ∆0 cos(2θ) (2.2.1)

where ∆(k) is the superconducting gap at a given momentum vector k, ∆0 the max-

imum gap value and θ the polar angle with respect to the crystallographic a-axis

direction. The order-parameter is characterized by the following:

1. It drops to zero at 45o from the main axis (the node direction).

2. The phases in the neighboring lobes differ by π. Here, we define the phase, φ , to

be:

eiφ =∆(∆0, θ)

|∆(∆0, θ)|(2.2.2)

In the following sections we discuss the implications of an anisotropic order-

parameter and, in particular, the impact of d -wave symmetry on tunneling exper-

iments. Subsequently, we show how tunneling experiments can be used to study

changes in the order-parameter symmetry.


π/2

3π/2

π 0

+

+

−−

[100]

[010]

Figure 2.1: Schematic representation of the d -wave order-parameter in a polar k-space. Neighboring lobes differ by π in phase and the order-parameter drops to zeroat 45o between the principal axes.

2.3 Andreev - Saint-James reflections and bound

states

In this section, we consider the quasi-particle states in the vicinity of a Normal

metal/Insulator/Superconductor (NIS) junction. In order to find the quasi-particle

states, we use the Bogeoliubov - de Gennes (BdG) equations. The quasi-particle

states are expressed by a two-component wave function in the form:

ψ =

[

u(r)

v(r)

]

(2.3.1)

2.3. ASJ reflections and bound states 7

Where u(r) and v(r) are the electron and hole wave functions respectively. As-

suming that the superconducting gap depends on the relative coordinates of the pairs,

s, the BdG equations can be written as:

Eu(r1) = h0(r1)u(r1) +

∫

dr2∆(s, r)v(r2) (2.3.2)

Ev(r1) = −h0(r1)v(r1) +

∫

dr2∆∗(s, r)v(r2) (2.3.3)

here, E is the energy measured from Fermi energy, ∆(s, r) the pairing potential where

s ≡ r1 − r2, r ≡ (r1 + r2)/2 and h0 = − ~2

2m∗∇2−EF +UHF (r). Here, EF is the Fermi

energy and UHF the Hartree potential. Taking the approximation that the Fermi

surface wave vector is constant in magnitude but only changes in its direction (kF ),

the BdG equations become:

Eu(r, kF) = h0(r)u(r, kF) + ∆(r, kF )v(r, kF ) (2.3.4)

Ev(r, kF) = −h0(r)v(r, kF) + ∆∗(r, kF )u(r, kF ) (2.3.5)

In this approximation we consider that:

∆(r, kF ) =

∫

dse−ik·s∆(s, r) (2.3.6)

Now, we proceed to examine the possible types of scattering of an electron injected

into the superconductor from a normal metal. If the electron has an energy equal to

or larger than that of the superconducting gap, there are four different possibilities:


Figure 2.2: Schematic illustra-tions of the reflection and trans-mission processes at the inter-face in a two-dimensional model.Here, the quantities φ and αexpress the injection angle ofthe electron and the angle be-tween the normal vector of theinterface and the x-axis of thecoordinate system in which wewrite the pairing potential, re-spectively.

1. Transmission as an electron-like quasi-particle

2. Transmission as a hole-like quasi-particle.

3. Reflection as an electron.

4. Reflection as a hole and the transmission of a Cooper pair.

While the first three processes are more trivial, the last is known as the Andreev

- Saint-James (ASJ) reflection.[5–8] It is worth mentioning that when the injected

electron has an energy smaller than the superconducting gap the first two processes

are prohibited, while the other two are still possible. A schematic representation of

these processes is shown in Fig. 2.2.

In order to calculate the amplitudes of the wave functions, or the probability for

each type of scattering, we solve the BdG equations within the desired boundary

conditions. Following Blonder, Tinkham and Kalpwijk (BTK) for the case of an

NIS junction and an isotropic order-parameter, we find the wave functions on the


normal side assuming that the current is preserved.[9] Taking into account the possible

trajectories, the expected wave function of the quasi-particle could be written as:

Ψ(x) =

(

u(x)

v(x)

)

=

eik+

Nx

1

0

+ a0(E)eik−

Nx

0

1

b0(E)e−ik+

Nx

1

0

, x > 0

c0(E)e−ik+

Sx

u

ve−iφ

d0(E)e−ik−

Sx

v

ue−iφ

, x < 0

(2.3.7)

~k±N =

√

2mEF ± E, ~k±S =

√

2mEF ± Ω

u =

√

E + Ω

2E, v =

√

E − Ω

2E, Ω =

√

E2 − ∆20

where a0(E), b0(E), c0(E) and d0(E) correspond to the coefficients for ASJ reflection,

normal reflection, transmission of electron and transmission of hole like quasi-particle

respectively. We assume that the order-parameter drops to zero at the boundary in

the form:

∆(x, kF ) = ∆0Θ(x) (2.3.8)

Here Θ(x) is the Heaviside step function. The potential barrier at x = 0 is modelled

by Hδ(x), in which H is the amplitude of the delta function. At the boundary, the

wave function should be continuous but its derivative should not be due to the delta


function potential. Thus:

Ψ(x)∣

∣

x=0+= Ψ(x)

∣

∣

x=0−(2.3.9)

dΨ(x)

dx

∣

∣

x=0+− dΨ(x)

dx

∣

∣

x=0−=

2mH

~2Ψ(x) (2.3.10)

Taking into account the fact that the Fermi energy is much larger then the en-

ergy E, and assuming that all wavelengths are approximately equal to the Fermi

wavelength, BTK obtained the following coefficients for an s-wave superconductor:

a0(E) =uve−iφ

(1 + Z2)u2 − Z2v2, b(E) =

Z(i + Z)(v2 − u2)

(1 + Z2)u2 − Z2v2(2.3.11)

c0(E) =(1 − iZ)u

(1 + Z2)u2 − Z2v2, d0(E) =

(1 − iZ)u

(1 + Z2)u2 − Z2v2

Z =mH

~2kF

However, as discussed in the previous section, in the case of cuprates HTS with the

d -wave order-parameter symmetry, one must take into account the change in phases

and amplitudes of the order-parameter in the calculation. This modification of the

BTK theory was carried out by Kashiwaya et al. in 1995. [10] In this case, we are

obliged to take into account the angle, θ, between the injected electrons and a normal

to the surface of the superconductor and with respect to its’ crystallographic direction

(due to possible different phases of the order-parameter at different directions). The


description for the injected electrons used here differs from that used in the isotropic

case: the wave vector now has the form:

k+N

= k+N(cos θ, sin θ) (2.3.12)

The electron and the hole-like quasi-particle, having different wave vectors, experi-

ence different effective paring potentials, which we denote as ∆+ and ∆− respectively.

As we have previously shown in equation 2.2.2, the phases could also be calculated

and we note them as φ+ and φ−. The wave functions can now be rewritten in the

following form:

Ψ(x) =

eik+

N·r

1

0

+ a0(E, θ)eik−

N·r

0

1

b0(E, θ)e−ik+

N·r

1

0

, x > 0

c0(E, θ)e−ik+

S·r

u+

v+e−iφ+

d0(E, θ)e−ik−

S·r

v−

u−e−iφ−

, x < 0

(2.3.13)

Taking into account that the system has translational symmetry along the direc-

tion parallel to the interface, Kashiwaya et al. rewrote the pairing potential from

Eq. 2.3.8 in the form:

∆(r, kF ) = ∆0Θ(x) (2.3.14)

Thus, using the BdG equation, the boundary conditions given by 2.3.9 and the


same approximation used before, namely that all wave vectors have the same magni-

tude, we can follow Kashiwaya et al. and find the following coefficients:

a(E, θ) =eiφ+u−v+

(1 + Z2)u+u− − Z2v+v−ei(φ−−φ+)(2.3.15)

b(E, θ) =Z(i + Z)(v+v−ei(φ−−φ+) − u+u−)

(1 + Z2)u+u− − Z2v+v−ei(φ−−φ+)

c(E, θ) =(1 − iZ)u−

(1 + Z2)u+u− − Z2v+v−ei(φ−−φ+)

d(E, θ) =ei(φ−−φ+)iZv+

(1 + Z2)u+u− − Z2v+v−ei(φ−−φ+)

Z =mH

~2kF cos θ

These coefficients are the basic quantities required for simulating a tunneling

process. In the following section we show how to reconstruct the tunneling cur-

rent from the above and evaluate the order-parameter and other quantities of the

superconductor under investigation.

However, an additional process may occur on the surface of the superconductor,

the formation of surface bound states, as first noted by Hu.[11] In order to understand

this process, we shall assume that a normal conducting layer, of thickness dn, exists

at the interface between the superconductor and the insulating barrier.

When an electron travels in a closed path in this normal layer and returns to

its origin with the same phase (or with a 2nπ difference with respect to its original

phase, when n is an integer), a surface energy bound state will emerge. Such a closed

path is illustrated in Fig. 2.3, where an electron travels from one end of the normal


Figure 2.3: Trajectory of an electron in a normal layer on top of a superconductor.First, the electron is ASJ’s reflected as a hole by the potential |∆1e

iφ1 |. Therefore, thehole undergoes normal reflection at the edge of the normal metal and travels towardsthe N/S interface where it is ASJ reflected as an electron, this time by the potential|∆2e

iφ2 |. The electron is then normally reflected by the normal metal thus returningto its original trajectory but with a different phase. The electron trajectory (solidline), hole trajectory (dotted line) and arrow mark the direction of particle movement.

layer towards the superconductor. Then, it is ASJ reflected and subsequently a hole

follows the same path with opposite velocity. Next, the hole is specularly reflected at

the normal surface and travels towards the superconductor. At the superconductor’s

boundary, the hole is ASJ reflected and, again, we are at the origin of the cycle with

an electron.

Thus, we must add all processes modifying the phase of the travelling quasi-

particle. The first ASJ reflection will contribute:

δΦ1 = − arccos

(

E

∆1

)

− φ1 (2.3.16)


The second phase change will be:

δΦ2 = − arccos

(

E

∆2

)

+ φ2 (2.3.17)

Here we consider that the effective pairing potential and the phase for each reflec-

tion could be different due to the anisotropic behavior of the order-parameter. Next

we consider the phase difference due to the propagation in the normal layer where

the phase should differ with respect to the total voyage length (approximately 4dn).

This results in the following change in phase:

δdn= 2dn(ke

N − khN) (2.3.18)

However, the Fermi wave numbers could be estimated by:

ke,hN = kF ± E

~vF

(2.3.19)

where ± represents the electron and hole respectively. The last contribution is cred-

ited to the normal reflection at the end of the normal layer. However, since the process

involves both electron and hole reflections, they cancel each other out.

Next, we search for the zero energy solution and find the condition in which a

bound state emerges. A simple calculation leads us to the following equation:

δΦ(E = 0) =π

2− φ1 +

π

2+ φ2 = π − (φ1 − φ2) = 2nπ ⇒ φ1 − φ2 = π (2.3.20)

Thus, in order to achieve a zero energy bound state, the difference between the

two phases in each ASJ reflection must be π. In the case of a d -wave superconductors

2.4. Tunneling experiments 15

such constructive interference will occur at the nodal-directed surface, i.e. the [110]

direction. It is apparent that when performing tunneling experiments, these bound

states have great importance, as will become evident in the following section, since it

serves as a direct probe for the symmetry of the order-parameter.

2.4 Tunneling experiments

Since the early stages of superconductivity it has been shown that tunneling can serve

as an excellent tool to measure the basic superconductivity quantities.[2] Bardeen’s

“golden rule” was the first approach used to treat the tunneling problem and resulted

in the following formula:

PLR = (2π/~)|M |2NR(1 − fR) (2.4.1)

were PLR is the tunneling probability for transition from a state to the left of the

barrier to a state on the right, |M |2 the matrix element for the transition, NR the

density of states on the right side, and (1− fR) the probability that the state on the

right side is empty.

For a normal metal, acting as a free electron gas, the matrix element contains

a factor which is inversely proportional the density of states, making the tunneling

probability insensitive to the normal metal’s density of states.

However, in the case of a superconductor electrode, it is obvious that one should


use the superconducting density of states in Eq. 2.4.1. Assuming that the matrix

element does not change when a metal becomes superconducting, it has been shown

that, although the tunneling probability is insensitive to the changes in the normal

state density of states, it can be used as a powerful tool to investigate the density of

states in the superconductor, since it is directly proportional to it.

For an s-wave superconductor, an intuitive result for a tunneling experiment would

be the following: as long as the voltage across the tunneling junction is less than the

superconducting energy gap, ∆, no current will flow. However, if the voltage across

the junction exceeds ∆, then the tunneling current would be as in the case of a normal

metal/normal metal tunneling junction, i.e. linear with voltage (Ohm’s law). Taking

into account that the total number of states should sum up to a constant value, it

is not surprising that the differential conductance of a superconductor/normal metal

would have a U-shaped behavior, with peaks at the energy gap, as seen in Fig. 2.4(d).

Considering that an experiment, unfortunately, cannot be carried out at absolute

zero temperature, we are obliged to take into account the temperature effect on the

population of the energy density of states, and hence to include the Fermi distribution

function, denoted as f(E, T ). Then, following the definitions in Eq. 2.3.11 for an ideal

tunneling junction (Z >> 1), the tunneling current has the form:

INS = CNN

∫ ∞

−∞

|E|√E2 − ∆2

< f(E) − f(E + eV ) > dE (2.4.2)


Here, INS is the tunneling current, e is the electron charge, 2∆ is twice the su-

perconducting energy gap and CNN is the conductance when both electrodes are

in their normal states. Since, in most cases, one is interested only in the normal-

ized conductance, i.e. the ratio between superconducting/normal metal and normal

metal/normal metal conductances, the exact form of CNN is irrelevant.

In April 1982, Blonder, Thinkham and Kalpwijk published a paper in Physical

Review B entitled: “Transition From Metallic to Tunneling Regimes in Supercon-

ducting Micro-Constrictions - Excess Current, Charge Imbalance, and Super-Current

Conversion”.[9] This paper, which had been quoted more then 1000 times, had a great

impact on superconductivity research, since it discusses all the mechanisms, such as

the ASJ reflections and gives equations for simulating the tunneling conductance.

Furthermore, as shown in the previous section, one of the BTK’s parameters is the

barrier strength through the dimensionless parameter Z (see definition in Eq. 2.3.11).

This parameter alters the spectra dramatically at different values (see Fig. 2.4). It

allows one to gain additional information on the different transport mechanisms by

varying the transparency of the junction from a fully metallic contact (Z = 0) up to

the extreme tunneling region (Z ≫ 1).

By January 1995, Kashiwaya et al. [10], following the work of Hu [11], expended

BTK’s theory to the case of an anisotropic paring potential, which is the case in

cuprate High-Tc superconductors. In this case, it is vital to take into account the


Figure 2.4: Tunneling conductance according to the BTK theory. For highly transpar-ent junctions (Z ≪ 1), the conductance below the gap approaches twice the normalconductance while, in the case of a strong barrier (Z ≫ 1), the U-shape behavior ispresent where no excitations below the gap are allowed. Adopted from the originalBTK paper [9].


Figure 2.5: Tunneling conductance for different tunneling directions (α) accordingto the Kashiwaya model for a d -wave order-parameter. The calculation made forT = 0, Z = 10, and tunneling cone of 20o. The zero bias conductance peak fortunneling in the node direction (α = 45o) and a gap feature for lobe directed (α = 0o)tunneling is observed. Adopted from [10]

.

direction in which the tunneling-injected electrons propagate with respect to the

order-parameter.

An additional parameter that must be taken into account is the effect of the tun-

neling cone. This cone represents the probability of an electron, injected from the

normal layer, to tunnel throughout the insulating barrier as a function of the angle

with respect to a normal to the surface. Since the tunneling probability decreases

exponentially with distance, electrons will enter the superconductor with an exponen-

tially decreasing probability with the cosine of the cone angle. For a clean metallic


contact, the cone would be wide open while, for a thick insulating layer, the tunneling

will be highly directional.

Kashiwaya’s theory enabled the calculation of the tunneling density of states for

different parameters sets, and thus the exploration of the properties of the cuprates

via tunneling measurements. As seen in Fig. 2.5, for a pure d -wave order-parameter

symmetry, different tunneling directions lead to totally different results. When tun-

neling in the lobe direction, such as [100], we find the traditional U-shape behavior

as in the case of the isotropic order-parameter. This is due to the high directionality

of the tunneling electrons. Measuring the bias value of the peak gives us the value of

the superconducting energy gap maximum, previously noted as ∆0.

As for tunneling in the node direction, such as [110], a Zero-Bias Conductance

Peak (ZBCP) dominates the whole spectrum. This is a direct result of the previ-

ously discussed ASJ bound state, and it has become one of the fingerprints of the

d -wave symmetry. These states were first discussed by Hu [11] and first observed

experimentally by Lesueur et al.[12]

The ZBCP is a direct probe for the phase difference in the ASJ cycle. This

fact greatly serves our research, since its measurment can probe changes in the order-

parameter symmetry. Simulation of the tunneling density of states using Kashiwaya’s

formalism [10] shows that in the presence of an additional imaginary order-parameter,

such as is or idxy, the ZBCP splits into two peaks, as shown in Fig. 2.6.


-2 -1 0 1 20

2

4

6d

xy/d

x2-y2

0 0.1 0.2

dI/d

V (a

.u.)

eV/ d

Figure 2.6: Theoretical calculation of tunneling conductance in the [110] directionfor a d + idxy order-parameter.[10] Parameters for the calculation are: tunnelingcone=20o, Z = 7 at zero temperature.


This result is of interest to us, since it was shown that the ZBCP actually splits

under certain conditions, such as an applied magnetic field, and spontaneously in

over-doped YBa2Cu3O7−x thin films [12–20]. Systematic tunneling measurements

may reveal whether a secondary channel, apart from the one responsible for the d -

wave symmetry, needs to be taken into account for a general theory for high Tc super-

conductivity. The possible theoretical explanations for the experimentally observed

ZBCP splitting will be discussed in the next section.

2.5 Splitting of the Zero Bias Conductance Peak

Lesueur [12] was the first to experimentally show that the ZBCP splits in the presence

of a magnetic field. Misinterpreted as a Zeeman splitting due to magnetic impurities,

it was later shown, by Krupke and Deutscher [15] and Aprili et al. [21], that the

ZBCP splits only if the magnetic field is applied perpendicular to the CuO2 planes.

This result ruled out the magnetic impurities Zeeman splitting scenario. Such an

effect is expected to be isotropic.

We divide the possible theoretical explanations into two main subgroups:

1. A Doppler shift to the energy of the surface-bound state.

2. Induced node removal in the presence of a magnetic field.

As we show below, the subgroups produce different field dependencies. This will

be used in our discussion in the following chapters.

2.5. Splitting of the Zero Bias Conductance Peak 23

2.5.1 Doppler shift

Rainer et al. studied quasi-particle excitations in the core of an isolated s-wave

vortex.[22] They found that, for clean high-κ superconductors, a transport current

through the vortex core (as well as a circular current around the vortex core) is carried

by localized states bound to the core by ASJ scattering, and not by normal electrons,

as is the case of traditional dirty high-κ superconductors. They showed that the

bound states in the vortex core exhibit a Doppler shift of their energies, δǫ = vF ·ps,

in the presence of a phase gradient in the order-parameter (or superfluid momentum,

ps). Here vF is the Fermi velocity.

The total current is obtained by adding both the positive (negative) shifts from

quasi-particles co-moving (counter-moving) with respect to the current flow. The

current profile of the bound state is thus different from the bulk super-current, in

particular it has an opposite direction in the vortex core.

The effect of surface Meissner currents

Following Rainer et al. work, Fogelstrom et al. [23] studied the effect of Meissner

currents on ASJ-bound states in a d -wave superconductor surface. Here, the iso-

lated vortex was “spread” along the surface, and the bound state is created by the

d -wave symmetry at the node-directed surface as calculated by Hu.[11] As in the case

of Rainer et al. , the bound state current is opposite to the bulk screening current and

decays over a few coherence lengths from the surface. In order to find the superfluid


Figure 2.7: (a) The total current density in different applied fields for a pure dx2−y2

order-parameter and a specular (110) surface. The current density heals to the Lon-don screening current, j ≃ (c/4π)Hλ, for x > 5ξ0. For x < 5ξ0, the current reversessign and is carried by the bound states. (b) The tunneling conductance vs. H forT = 0.3Tc and a tunneling cone of 45o. The splitting of the ZBCP reflects the shiftin the surface bound states by the screening current at x = 0. The inset shows thelinear splitting of the ZBCP at low fields. Adopted from Fogelstrom et al.[23].

momentum, we assume a constant bulk current density and no nearby vortex influ-

ences. From the London equation, we find the relation between the magnetic field

and the current density for ξ0 ≪ x ≪ λ:

j(x) ≃ (c/4π)Hλ (2.5.1)

Then, the shift in the bound state, as observed in the tunneling experiment with

a tunneling cone of θc, is:

δ(H) = (e/c)vFHλ sin θc (2.5.2)

The total current density and the Doppler shift effect on the nodal tunneling

spectrum are shown in Fig. 2.7. This model predicts that the ZBCP splitting will be


linear with the magnetic field up to a certain field where the current density reaches

the depairing limit. This field is roughly the thermodynamical critical field, HC ,

which is of the order of 1 Tesla in YBa2Cu3O7−x . Beyond that field, the Doppler

effect, and therefore the ZBCP splitting, saturate.

As mentioned, this model assumes that the screening current is given by the field

from the London equation. Taking into account a surface barrier, such as the Bean-

Livingston barrier,[24–26] it is possible that the Meissner currents, in a given field,

are different in increasing and decreasing magnetic fields. This will be discussed in

detail in chapters 4 and 5.

The effect of an isolated vortex

In the previous section, we discussed the effect of a surface Meissner current on the

ASJ bound states and ignored the contribution from nearby vortices. This assumption

is valid as long as the field is low enough.

Graser et al. studied the complementary effect of an isolated vortex at a distance

xV from the surface, neglecting the influence of the surface Meissner current.[27, 28]

They found that the local density of states is highly influenced by the vortex presence.

The effect is governed by a local Doppler shift from the vortex currents. Here, in

contrast to the previous model, the Doppler shift depends on the distance of the

vortex from the surface. As the vortex approaches the surface, the effective currents

increase and therefore the effective Doppler shift will be larger. This will show up as


Figure 2.8: Quasiparticle spectrum of a d -wave superconductor taken at a (110)boundary at the point adjacent to the vortex center. The curves are calculated fordifferent vortex distances xV from the boundary. Adopted from [27].

an increasing ZBCP splitting in the tunneling density of states.

In contrast, almost no effect on the density of states will be induced by the vortex

for a [100] surface or in the case of an s-wave superconductor. The local density of

states for various vortex distances from the surface is shown in Fig. 2.8.

However, Graser et al. did not calculate the tunneling current which must take

into account the tunneling cone. This will effectively lower the splitting value at any

given distance. Furthermore, the distance for the nearest vortex to the surface could

be different for a given field due to surface barriers.[24–26] In general, the Doppler

shift effect for the vortex will be opposite to that of the Meissner effect since both

current flow in opposite directions.


Assuming a uniform distribution of the vortices, a rough estimate for the distance

of the first vortex to the surface would be:

xv/ξ ∝√

H/Hc2 (2.5.3)

Here H is the applied field and Hc2 is the upper critical field. Assuming that

the vortex currents induce similar ZBCP splitting (δ), as in the case of Fogelstrom

et al. [23], the effect of the vortex proximity induces a splitting:

δ(H) ∝√

H/Hc2 sin θc (2.5.4)

2.5.2 Induced node removal

Unlike conventional superconductors, in a high Tc superconductor, the dominant

order-parameter symmetry is d -wave .[4] This symmetry has node lines, located 45o

to the main principle axes, where the energy gap drops to zero. This is the supercon-

ductor’s “weakest-link in the chain” since quasi-particles can easily be excited along

these lines. Several authors investigated a possible node-removal mechanism induced

by the presence of a magnetic field.

The first to introduce such a mechanism was Laughlin [29] who formulated a free

energy term, which includes a second component to the order-parameter, in the form

of idxy. Such a component breaks both time reversal and parity symmetries as it

involves boundary currents along the surface. These currents produce a magnetic


moment which couples to the applied magnetic field. Moreover, the free energy must

include the cost for removing the node which is proportional to the cube of the induced

gap (at the zero temperature limit). Minimizing the free energy, Laughlin found that

the induced gap value will be:

∆dxy(T → 0) = ~ν

√

2eB

~c(2.5.5)

Here, B is the applied field and ν is the root-mean-square velocity of the d -

wave node defined as:

ν =√

ν1νF (2.5.6)

where νF is the Fermi velocity and ν1 is the velocity at the node. Earlier, we defined

the d -wave gap in Eq. 2.2.1 to be ∆(θ) = ∆0 cos(2θ). Therefore, we can rewrite ν1

as:

ν1 =∂∆

~∂k|node ≃

2∆0

m∗νF

(2.5.7)

here ∆0 is the d -wave maximum gap and m∗ is the effective electron mass. Therefore,

we approximate the root-mean-square velocity to be:√

2∆0

m∗. Plugging that into Eq.

2.5.5 we get:

∆dxy(T → 0) = 2

√

∆0~eB

m∗c= 2

√

∆0~Ωc (2.5.8)

here Ωc = eH/m∗c is the cyclotron frequency. In order to calculate the effect of the

imaginary component on the tunneling spectrum, we use the formalism of Kashiwaya

et al. [10] with an order-parameter of the form ∆dx2

−y2+ i∆dxy

. The additional dxy


kx kyelectron trajectory

hole trajectory

Figure 2.9: Schematic illustration of a the ASJ cycle for nodal Larmor precessingquasi-particle in the presence of a magnetic field applied perpendicular to the page.

gap will lead to a ZBCP splitting where the split peak position is set by the amplitude

of the imaginary gap (see Fig. 2.6).

A different approach for analyzing the behavior of quasi-particle excitations in

the presence of magnetic fields was introduced by Gor’kov and Schrieffer [30] and by

Anderson [31].

They consider the effect of the magnetic field (Hc1 ≪ H ≪ Hc2) along the c-axis

that causes a Larmor precession of nodal quasi-particle excitations. The quasi-particle

trajectory along the node line is bent due to the Lorentz force until its energy is equal

to the d -wave gap at that angle. Then, the quasi-particle undergoes an ASJ reflection

and a hole is reflected to undergo the same process with an opposite velocity.

Therefore, we now have a full ASJ cycle in the presence of a magnetic field which

produces a bound state in the vicinity of the node line. A schematic illustration of

this is shown in Fig. 2.9. The bound state from reflections by the d -wave gap has


discrete allowed energy levels:

En = ±2√

n∆0~Ωc (2.5.9)

where n is an integer and ∆0 is the maximum d -wave superconducting gap. We

note that the first energy level (n = 1) of Gork’ov-Schrieffer or Anderson is identical

to Laughlin’s additional complex order parameter, ∆dxy, although the reasoning is

completely different.

Janco [32] followed Gor’kov-Schrieffer’s work and pointed out that these levels

should be observable using a scanning tunneling microscope at the Wigner-Seitz cell

boundaries of the vortex lattice, where the superfluid momentum is zero. Tunneling at

any other location will cause the levels to be smeared, as they will be Doppler-shifted

by the circulating currents. However, we note that a constant superfluid velocity, in

the first approximation, will be additive to the Hamiltonian and will therefore only

shift the energy levels by a constant.[31]

Chapter 3

Experimental setup

This chapter describes the experimental setup used throughout this work. We begin

with thin films preparation method and continue following the track that each sample

passed from tunneling junctions fabrication through various electrical, microscopy and

spectroscopy measurements and analysis.

3.1 Thin film deposition

In this work, we deposit YBa2Cu3O7−x thin films using RF and DC sputtering system.

Driven by the desire to study effects related to the anisotropic nature of the d -

wave superconductor, two different films orientations were used - the (110) and (100)

films orientations.

We followed the growth procedure for these orientations as described in details

by R. Krupke [33] and Y. Dagan [34]. Both film’s orientation growth procedure

are similar with one expection - the single crystals substrates. For (110) oriented

31

32 Experimental setup

films we used SrTiO3 substrates while for the (100) orientation we used LaSrGaO4

substrates. In both cases the substrates had the [001] direction along one edge of

the sample and therefore allowed us to have a well defined c-direction along that

edge in the YBa2Cu3O7−x thin film. The substrates we used were typically 5x10mm

rectangulars, however smaller films sizes made no significant different on the outcome

of the experiments.

The substrates were first cleaned by Ethanol and later by Acetone using ultrasonic

cleaning apparatus. In order to remove the chemicals and to dry the substrate we

used dry nitrogen gas flow. Then the substrate was glued to a stainless steel plate

using silver paint. The plate was then placed on top of the heater itself placed inside

the vacuum chamber. Next, the chamber was pumped down to a typical pressure of

2-4·10−6mbar while the heater was gradually heated up to 700oc. After the chamber

was properly evacuated and the substrate was stable at the right temperature, we

controlled the pumping rate in order to reach the desired working pressure while

keeping an environment of 50% Ar and 50% O2 gases in the chamber.

Next, in order to reduce the (103) orientations in the sample, a 600 A thick (1

hour deposition) buffer layer of PrBa2Cu3O7−x was first deposited using off-axis RF

sputtering in a pressure of 80 mTorr [33–35]. Subsequently, at the same pressure, a

thin layer of YBa2Cu3O7−x was deposited using an off-axis DC sputtering. This layer

was about 100 A and was deposited for 10 minutes. Then, the pressure was rapidly

3.2. Tunneling junction formation and measurement 33

raised to 160 mbar and the thin film deposition of YBa2Cu3O7−x was started at that

conditions.

At the end of the film deposition, the sample was rapidly cooled down, using a

direct flow of O2 gas at a pressure of about 700 Torr.

3.2 Tunneling junction formation and measurement

It is extremely important to have clean surfaces for reliable tunneling measurements,

as it probes the surface density of states. The cuprates are notorious for their fast

surface degradation. This is why, most tunneling junctions are made after various in-

situ cleavage techniques. However, such techniques have thier limitations, as cleavage

is limited mainly to the CuO planes. Therefore it is practically impossible to perform

tunneling studies on different directions as we did in this work.

An alternative is to make tunneling junctions using photolithography techniques.

Though, some limited success has been reported, imbedding the samples into polymers

and chemicals involved in this technique usually damages the surface under study.

R. Krupke showed that when a small indium wire is pressed against the surface of

freshly made YBa2Cu3O7−x thin film, a tunneling junction is naturally formed [15]. It

appears, that the indium adsorbs some oxygen from the surface which creates a thin

dielectric barrier, of indium oxide, between the sample and the indium. The contact

areas are about 0.5 mm2 and a typical junction’s resistance ranges from a fraction


Figure 3.1: Schematic illustration of a (110) film and indium tunneling junctionconfiguration.

of to several Ohms. The junctions are very stable over time (a few weeks) and can

undergo many thermal cycles without significant changes in the tunneling spectra.

Several contacts and junctions to the samples can be made using the same procedure,

however, after a few minutes out of the vacuum chamber, the surface degrades and

the indium impossible does not bond anymore. A schematic illustration of the film

and junction is presented in Fig. 3.1

Later, the sample is mounted on a probe and electrically connected with copper

wires in a four terminal configuration (see Figs. 3.1). The probe is lowered into

an helium Dewar in which an Oxford instrument 6 T superconducting magnet is

installed. At low temperatures, when the sample is superconducting, the junction

spectra is obtained digitally, by sending current from a 224 Keithley source and

measuring the voltage drop with 3456A HP voltmeter. In order to measure few

3.3. Film characterizations 35

Figure 3.2: Photos of indium tunneling junctions on top of a YBa2Cu3O7−x films.

junctions in series, a Keithley 708 switching system is used. The whole system is

controlled by a computer and a National Instrument Labview program. In some high

magnetic fields measurements, different current sources and voltmeters were used,

having similar specifications. We emphasis that all tunneling spectra, dI/dV (V),

shown in this work, are digitally obtained, without any smoothing or filtering, by two

points differential calculation from the V(I) curved directly measured in the form:

dI

dV(Vi) =

Ii − Ii+1

Vi − Vi+1

(3.2.1)

where, Vi = (Vi + Vi+1)/2 is the i’th current and voltage measurements in the V(I)

scan.

3.3 Film characterizations

In order to characterize the films quality and crystallographic orientation several

measurements where performed.


0

3092 94

0.0

0.2

0 50 100 150 200 250 30005

10152025303540

T(K)

Rc(

)

0.00.10.20.30.40.50.60.70.8

x x

Rab (

)

c-axis

1 2

3 4

Figure 3.3: R(T) measurement of an optimally doped YBa2Cu3O7−x thin films. Thefilm’s resistivity was measured parallel and perpendicular to the CuO planes. Thetwo directions are measured by measuring the resistance in different configurationsas explained in the text. Top insert shows the square contact configuration.

3.3.1 Resistivity measurements

The sample crystallographic orientation is such that the [001] direction is oriented

along one edge of the sample and the [110] or [100] direction is along the other. Since

electrical transport is profoundly different along the c-direction and the a-b planes,

comparing resistivities, and in particular their temperature dependent, along both

directions, provides strong evidence for the films’ epitaxial growth and its crystallo-

graphic anisotropic nature.

Using a square geometry (see insert in Fig. 3.3) enables one to measure both


in-planes resistivities. For example, for measuring the c-axis resistivity, current will

be flown from contact 1 to 2 while voltage will be measured between contacts 3 and

4. Alternatively, for the a-b resistivity measurements, the current will be flown from

contact 1 to 3 while voltage will be measured between contacts 2 and 4. As shown

in Fig. 3.3 there is a difference of two orders of magnitude in resistivity between the

two orientations and the temperature dependencies are completely different.

Furthermore, previous works showed that R(T) measurements in the a-b planes

vary with sample doping. For overdoped samples it has a positive curvature [36–38],

becomes linear at optimum doping and exhibits downward deviation from linearity

as the sample enters the pseudo-gap region in underdoped samples [38, 39].

3.3.2 Microscopy and spectroscopy measurements

For additional verification regarding the films’ quality and crystallographic orientation

we imaged the films surfaces using Scanning Electron Microscope (SEM) and Atomic

Force Microscope (AFM). Images of films’ surfaces exhibit many important features.

To begin with, the in-plane crystallographic orientation could be easily demonstrated.

In Fig. 3.4 we show SEM and AFM images taken for a thin YBa2Cu3O7−x film. There

a ‘chocolate fingers’ structures oriented perpendicular to the c-axis direction is clearly

demonstrated. Moreover, one could study the amount of out-growths, usually CuO

and BaCuO2 particles, resulting mainly from high oxygen partial pressure (for more


Figure 3.4: (a) SEM and (b) AFM images taken for a thin (110) orientedYBa2Cu3O7−x thin films.

details see [33]). Last, AFM topographic images showed that films roughness ranged

between 20-100A and that thin films had significantly more holes in comparison to

thick films.

Finally, we used a two angle x-ray diffractometer (θ−2θ scan) to measure the film

out-of-plane crystallographic orientation. In Fig. 3.5 we show a typical x-ray scan

where the YBa2Cu3O7−x peaks are clearly shown.


0 20 40 60 80 100 12010

100

1000

10000

100

33

100

112

PBCO (330)

YBCO (110) YBCO (220)

coun

ts(a

.u.)

2 (deg)

YBCO (330)

100

70

Figure 3.5: θ − 2θ x-ray diffractormeter scan for a (110) oriented YBa2Cu3O7−x thinfilms. The expected YBa2Cu3O7−x peaks are exposed and marked in the figure. EachYBa2Cu3O7−x peak is in proximity to the large substrate’s peak. The PrBa2Cu3O7−x

buffer layer peak could also be identified in large scanning angles.

Chapter 4

Origin of hysteresis in magnetic

field ZBCP splitting

As discussed in the chapter 2, tunneling experiments are a highly sensitive tool for ex-

amining the order-parameter symmetry. One of the fingerprints for the d -wave order-

parameter symmetry in the general case of cuprates, and YBa2Cu3O7−x in particular,

is the Zero Bias Conductance Peak (ZBCP), which is described in detail in section2.4.

In the case of a d -wave order-parameter, the tunneling conductance should be

sensitive to the crystallographic direction of the tunneling (see Fig. 2.5). Here we

assume that the electrons tunnel from the normal metal are spread within a narrow

range of k orientations around the direction perpendicular to the junction. This is

also known as the tunneling cone.

41

42 Origin of hysteresis in magnetic field ZBCP splitting

A correlation between surface topography and tunneling conductance was ob-

served using a Scanning Tunneling Microscope (STM) which probes the tunneling

density of states with nm resolution.[40]

In our work, we used a planar tunneling junction. For these, the films’ surface

roughness scale is smaller than the junction size and therefore results in similar tunnel-

ing spectra in different crystallographic directions in zero magnetic field. Moreover,

in such cases, the tunneling spectra show both the ZBCP originating from nodal

tunneling and a gap-like feature originating from an anti-nodal tunneling.[23]

In this work we studied ZBCP splitting in the presence of magnetic fields applied

perpendicular to the CuO2 planes, for two different crystallographic film orientations

in increasing and decreasing magnetic fields.

Since the growth procedures for both [110] and [100] oriented films are similar, we

grew and measured both films simultaneously using the procedure described in detail

in [33, 34]. This minimizes the difference between the films, other than the substrate.

In this paper [18] we show that, for a given field, the ZBCP split in the [110]

crystallographic film orientation is much larger from than that observed in the [100]

oriented film. Moreover, we studied the hysteretic behavior of the ZBCP splitting in

increasing and decreasing magnetic fields for both orientations. We claim that the

hysteresis behavior can be explained if we take into account the effect of the Bean-

Livingston barrier which is responsible for a much higher (lower) surface current in

43

increasing (decreasing) magnetic fields. In addition, we concluded that in order to

explain the large ZBCP splitting in a decreasing field in the [110] oriented films, it is

necessary to take into account an additional contribution to the splitting, other than

the Doppler shift effect of the zero energy surface bound state.

The full reference of the paper is: Beck, R., Kohen, A., Leibovitch, G., Castro,

H., and Deutscher, G. (2003) J.of Low Temperature Physics 131, 451.


45


47


Chapter 5

Order parameter node-removal inmagnetic fields

As shown in previous chapters, the Zero-Bias Conductance peak (ZBCP) serves as a

probe for the order-parameter symmetry and surface current strength via the Doppler

shift effect. In the previous chapter we showed that the ZBCP splits in the presence

of a magnetic field. We also showed that this splitting is much larger when tunneling

along the [110] direction than along to the [100] direction.

In this work [17], we study the tunneling spectrum of YBa2Cu3O7−x /indium

nearly optimally doped junctions at fields up to 16 Tesla. We find that the splitting

of the ZBCP in decreasing fields follows the law of δ↓(H) = A√

H. Here, H is the

applied magnetic field measured in Tesla, and A = 1.1 meV/√

T . This law holds for

different film thicknesses from 600 up to 3200A.

We show that while the data in increasing magnetic fields includes the Doppler

effect, the data in decreasing fields is consistent with theoretical models suggesting a

node-removal in the presence of magnetic fields.[29–31]

49

50 Order parameter node-removal in magnetic fields

The full reference of the paper is:

Beck, R., Dagan, Y., Milner, A., Gerber, A., and Deutscher, G. (2004) Phys.Rev. B

69, 1440506.

51

Order-parameter-node removal in the d-wave superconductor YBa2Cu3O7Àxin a magnetic field

Roy Beck,* Yoram Dagan,† Alexander Milner, Alexander Gerber, and Guy DeutscherSchool of Physics and Astronomy, Raymond and Beverly Sackler faculty of Exact Sciences, Tel-Aviv University, 69978 Tel-Aviv, Israel

~Received 4 September 2003; published 12 April 2004!

We have measured the in-plane tunneling conductance of optimally doped YBa2Cu3O72x films/In junctionsas a function of magnetic field and film orientation. In zero applied field all samples exhibit a zero biasconductance peak~ZBCP! attributed to thed-wave symmetry of the order parameter. In junctions formed on~110! oriented films, the splittingd↓(H) of the ZBCP in decreasing fields applied perpendicular to the CuO2

planes follows the lawd↓(H)5A•H1/2 with A51.1 mV/T1/2. This law is obeyed up to 16 T for film thicknessvarying from 600 Å~less than the London penetration depthl! up to 3200 Å~about twicel!. Since Meissnercurrents are negligible in decreasing fields and at thickness smaller thanl, this splitting cannot be attributed toa Doppler shift of zero energy surface bound states. The data taken in decreasing fields is quantitativelyconsistent with a field inducedidxy component of the order parameter. The effect of the Doppler shift isprominent in data taken in increasing fields and in the field hysteresis of the splitting.

DOI: 10.1103/PhysRevB.69.144506 PACS number~s!: 74.72.Bk, 74.50.1r

I. INTRODUCTION

The excitation spectrum of a conventional superconductor~low Tc) is characterized by an almost independent momen-tum s-wave energy gap,D. This is not the case in the highTc

cuprate superconductors; there it is broadly agreed that theground state superconducting order parameter~OP! isstrongly momentum dependent, being maximal in the direc-tion of the crystallographic axes a and b. In most cases, itappears to have the puredx22y2 symmetry, being zero at 45°between these axes~the node directions!, where it changessign. In contrast to the finite energyD required to excite alow energy quasi-particle in a low-Tc superconductor, such aquasi-particle can be excited with an infinitely small energyin a d-wave superconductor along the nodes. This is nolonger the case if an additional imaginary component ispresent in the OP. In this case, the energy spectrum of thesuperconductor is fully gapped.

Theoretically, it has been suggested that such an imagi-nary component can result from an instability of thed-waveOP under perturbations such as surface pair breaking,1

impurities,2 proximity effect,3,4 and magnetic field.5 Anotherview is that a phase transition occurs at a certain dopinglevel6,7 or magnetic field8 from a pured wave to a nodelessOP having thedx22y21idxy or dx22y21is symmetry. Thedxycomponent breaks both time and parity symmetries, hence itinvolves boundary currents that flow in opposite directionson opposite faces of the sample as previously pointed out byLaughlin.8 These currents produce a magnetic momentwhich, through interactions with the magnetic field, lowersthe free energy by a term proportional toB•dxy , whereB isthe magnetic field induction. On the other hand, in the zerotemperature limit, node removal costs an energy proportionalto idxy

3 . Minimization of the sum of the two contributionsleads to an amplitudedxy5A•B1/2, whereA is a coefficientgiven by Laughlin.

Experimentally, two sets of experiments have been inter-preted as indicating that a magnetic field, applied perpen-

dicular to the CuO2 planes, can indeed induce a nodeless OP.Measurements of the thermal conductivityk~H! onBi2Sr2CaCu2O8 ~Bi2212! single crystals have shown a de-crease followed by a plateau at a certain field.9 This field wasinterpreted as that beyond which a finiteidxy componentappears at the finite temperature where the experiment isperformed.8 The finite gap in the plateau region prevents theexcitation of additional quasiparticles. Field hysteresis of thethermal conductivity has, however, led to a controversy overthe actual origin of the plateau; to date, this issue has re-mained unresolved.10

A second set of experiments possibly indicating the oc-currence of a nodeless OP is the field evolution of the con-ductance of in-plane tunnel junctions formed at the surfaceof YBa2Cu3O72x ~YBCO! films oriented perpendicular tothe CuO2 planes.11 The conductance of in-plane tunnel junc-tions formed at the surface of YBCO films having that ori-entation presents a peak at zero bias~ZBCP!. This peak re-flects the existence of zero energy surface bound states thatcome about due to a change of phase byp upon reflection ata ~110! surface.12 Its split, often observed for instance undermagnetic fields applied parallel to the surface and perpen-dicular to CuO2 planes, may indicate the occurrence of afully gapped order parameter, having the symmetryd1id ord1is. The new peak positiond~H! would indicate the am-plitude of theid or is component. However there exists adifferent explanation of a field-induced split, in terms of aDoppler shift of the bound states energy.13,14The energy shiftis equal tovs .pF, wherevs is the superfluid velocity of theMeissner currents, andpF is the Fermi momentum of thetunneling quasiparticles.

In order to distinguish between these two possible inter-pretations, we have taken detailed data in decreasing fieldson ~110!-oriented films having thickness d, down to wellbelowl. At such thickness the Doppler shift should be muchreduced sincevs5elH•tanh(d/2l). Taking data in decreas-ing fields has also the effect of reducing Meissner currentsand the corresponding Doppler shift. This is because there is

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no Bean-Livingston barrier against flux exit~while there maybe a strong one against flux entry!.15

II. EXPERIMENTAL SETUP AND RESULTS

YBCO films near optimal doping, having thicknessesranging from 600 to 3200 Å, were prepared in the~110! and~100! orientations by the template method, using SrTiO3 andLaSrGaO4 substrates of the appropriate orientation.16,17

Critical temperatures of all films were in the range of 88–90K. Junctions were prepared by pressing In~Indium! pads ona fresh films surface.17,18 In almost 100% of the cases a goodjunction is formed by this method and theI(V) characteris-tics are reproducible. The junctions were measured at 4.2 K,and some were also measured at 1.6 K. All junctions dis-played an unsplit ZBCP in zero magnetic field, irrespectiveof the film orientation. The junctions’ characteristics weremeasured as a function of field, applied parallel to the sur-face, either parallel or perpendicular to the CuO2 planes~seeFig. 1 for the sample configuration and field orientation!.Measurements were systematically taken in increasing anddecreasing fields. Field splitting was only observed when thefield was applied perpendicular to the CuO2 planes, in agree-ment with previous results, confirming the uniaxial in-planeorientation of thec axis.18 A total of 20 junctions were mea-sured. A typical data set is shown Fig. 2 for a 600 Å,~110!-oriented film.

We first address the question of the origin of the hystereticbehavior in field apparent in Fig. 2. In general the split, for agiven field, is always higher in increasing fields. The peakposition for the same sample as in Fig. 2 is shown in Fig.3~a! in increasing and decreasing fields. In increasing fields,the peak position reaches about 4 meV at 5 T. At higherfields, the exact maximum point cannot be determined be-cause the peak becomes smeared, possibly because it mergeswith the main gap structure. We define the hysteresis ampli-tude as the differenceDd~H! between the peak position atincreasing,d↑(H), and decreasing field,d↓(H). For compari-son, this hysteresis amplitude is shown in Fig. 3~b! for twofilms with different thicknesses: 600 and 3200 Å. It is appar-ent that the hysteresis saturates at about 2 T in the 3200 Åfilm, a field of the order of the thermodynamical critical fieldHc . The hysteresis amplitude is larger for the thicker film,about twice as high as for the thinner film. This hysteretic

behavior can be understood within the Doppler shift modelof the ZBCP splitting,13 if we take into account the propertiesof the Bean-Livingston barrier. In samples thicker than theLondon penetration depth, this barrier prevents flux entry upto fields on the order of Hc . Up to that field, the superfluidvelocity of the Meissner currents increases almost linearly;beyond that field, it saturates. The Doppler shift, proportionalto the superfluid velocity, follows the same behavior. By con-trast, in decreasing fields, there is no barrier that preventsflux exit. This has been shown theoretically by Clem,15 veri-fied experimentally by Bussiere,19 and shown also to apply intunneling experiments by Moore and Beasley20 and in YBCOsystem by Xu.21 Hence, when the field is decreased, the sur-face superfluid velocity quickly reduces to zero, as does theDoppler shift. This is the origin of the hysteresis. The impli-cation is that by subtractingd↑2d↓ @Fig. 3~b!# one measures

FIG. 1. ~Color online! Schematic presentation of the measure-ment setup for the~110! films. Indium pads are pressed against thesurface of the oriented thin film. The crystallographic orientation ofthe film enables one to apply a magnetic field parallel or perpen-dicular to the CuO2 layers while it is been kept parallel to films’surface.

FIG. 2. ~Color online! Normalized dynamical conductanceG5dI/dV vs biasV for increasing~a! and decreasing~b! appliedmagnetic fields for an YBCO~110!-oriented film at 4.2 K. Filmcharacteristics:Tc588 K, film thicknessd5600 Å. The splittingdis defined as half of the distance between the positions of the con-ductance maxima. In increasing field it can be determined clearlyfrom a field of about 0.1 T up to 5 T, and in decreasing fields from13 T down to 0.9 T. Applied fields~in Tesla!: 0, 0.1, 0.3, 0.5, 0.7,0.9, 1.2, 1.5, 1.8, 2.1, 2.5, 3.0, 3.5, 5, 6, 7, 11, 13, and 15.~c!

Behavior of the same junction for magnetic field applied parallel tothe CuO2 planes at fields~in Tesla!: 0, 0.5,1, 2, 4, 8, 12, and 15.5.The strong anisotropy of the field effect confirms the good in-planeorientation of thec axis.

FIG. 3. ~Color online! Field splitting hysteresis curve for a~110!-oriented film in increasing~m! and decreasing~.! magneticfields. ~a! ZBCP splitting ~d! for a 600 Å thick film, and~b! thedifferenceDd5d↑2d↓ between the position of the ZBCP splittingin increasing and decreasing fields for~110! 600 Å ~full circles! and3200 Å~open circles! thick films at 4.2 K. This is a measurement ofthe Doppler shift effect~see the text!. The lines in~b! are a guide tothe eye.

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only the Doppler shift effect. The results in Fig. 3~b! are inqualitative agreement with the Doppler shift model predict-ing the saturation at fields higher than Hc for the thicker film,and the thickness dependence observed. The influence of theBean-Livingston barrier is, as expected, more apparent in thethicker film. As for the substantiald↓(H), it must find adifferent explanation.

Our central result is shown in Fig. 4, which presents pre-cisely the ZBCP splitting measured in decreasing fields for~110!-oriented films having thickness ranging from 3200down to 600 Å, plotted as a function of the square root ofthe applied field. Data for all samples follow the lawd↓

5A•AH, with A51.160.2 meV/T1/2. For reasons explainedabove, this behavior cannot be attributed to a Doppler shiftof the zero energy surface bound states. We attribute it tonode removal.

These results are quite different from those previouslyreported for~100! ~Ref. 17! and ~103!-oriented14,22,23films.Generally speaking, field splitting values are smaller forthese orientations. We demonstrate the difference betweentunneling into~100!- and~110!-oriented films in Fig. 5. Here,we present the splitting versus increasing magnetic field,

d↑(H), for two films differing only by their crystallographicorientation. While the~110! oriented film exhibits splitting of4.4 mV at 3 T, a splitting of only 1.1 mV is seen at the samefield in the ~100!-oriented film. Moreover, at high fields thesplitting has a different behavior in these two orientations. Inthe ~100! film d↑(H) almost saturates at fields higher than 1T, while in the~110! film the ZBCP keeps splitting rapidly. Inaddition, splitting values in the~100! orientation are stronglythickness dependent. For samples thinner than 1600 Å, wefind that they are too small to be determined experimentallyat 4.2 K up to 6 T~not shown!. These results are consistentwith a splitting dominated in the~100! orientation by theDoppler shift effect, with a different~additional! mechanismbeing responsible for the splitting behavior in~110!-orientedfilms.

III. DISCUSSION

Surface faceting is thought to be the reason for the ZBCPcommonly observed in~100!-oriented films.13 Recently,some direct evidence has been provided by scanning tunnel-ing microscopy measurements, suggesting that~110! facesare present in films of that orientation.24 We have shown thatwhile the zero field ZBCP is similar for both macroscopicorientations, their field-splitting behavior is entirely different.Our results demonstrate that in order to observe a substantialsplitting in decreasing fields and in films thinner than theLondon penetration depth—namely, under conditions wherethe Doppler shift effect is very weak—one must use sampleshaving the~110! orientation. Then, and only then, the experi-mental data show the H1/2 law in the entire field range stud-ied ~up to 16 T!, and at all film thickness. This stronglysuggests that node removal occurs, but only for that filmorientation. Although~100! films do have~110! facets attheir outer surface, the inner surfaces at the interface with the~100! LaSrGaO4 substrate and PrBa2Cu3O7 intermediatelayer presumably quite flat and have the~100! orientation.The presence of~110!-oriented surfaces on both sides of thefilm appears to be a necessary condition for node removal.

Our data are in agreement with the expression given byLaughlin for the amplitude of the field inducedidxy compo-nent, d5A•B1/2. Under our experimental condition, thinfilms and high magnetic fields, we can assume thatB5m0•H. The coefficient A in his theory is proportional to thesquare root of the gap and the Fermi velocity. For the com-pound Bi2212 he calculatesA51.6 mV/T1/2. Taking into ac-count the respective values of the gap in this compound~about 30 meV! and in YBCO~about 20 meV!, our experi-mental resultA51.1 mV/T1/2 can be considered to be ingood agreement. Yet, it must be emphasized that Laughlinhas not considered the effect of the orientation of the samplesboundaries. Therefore, one cannot say directly whether ourobservation that node removal only occurs in~110!-orientedfilms is in agreement with his model or not. For similar rea-sons, one cannot say whether there is a connection betweenour results and the thermal conductivity measurements ofKrishanaet al.9 carried out in a different geometry, whichLaughlin has interpreted within the framework of his theory.

In a previous publication,16 we reported ZBCP field split-

FIG. 4. ~Color online! ZBCP field splitting in increasing anddecreasing fields for~110! 600 Å ~full circles! having thicknessranging from 3200 to 600 Å, as a function of the square root of themagnetic field~H! applied parallel to surface and to the crystallo-graphicc axis. The line is a linear fit to all data points and has a1.1 mV/T1/2 slope.

FIG. 5. ZBCP field splitting measured in increasing fields for~100!- ~full triangle! and ~110!- ~empty triangle! oriented films.Film thickness is 3,000Å for both films and data taken at 4.2 K.

ORDER-PARAMETER-NODE REMOVAL IN THEd-WAVE . . . PHYSICAL REVIEW B 69, 144506 ~2004!

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ting data taken in increasing fields. We noted that the H1/2

behavior seen up to about 0.5 T is incompatible with theDoppler shift model, which predicts a linear behavior at lowfields. Likewise, we also noted that a field splitting that per-sists in films having a thickness of orderl or less is incom-patible with this model. We believe that the data presentedhere, particularly taken in decreasing fields and at evensmaller film thickness, reinforce this conclusion and make amuch more compelling case in favor of the node removaleffect.

In addition, we would like to point out that the absence ofZBCP field splitting in geometries different from ours maynow be understood. This is the case in grain boundaryjunctions25 and for junctions grown on single crystal edges.26

With the field applied perpendicular to the surface, vorticespenetrate at low fields, and there cannot be any substantialDoppler shift because there are no large screening currents.Second, the geometry of the boundaries is unfavorable forthe flow of Laughlin’s currents. It could be that the contra-dictory results reported in thermal conductivity experiments,concerning the existence of a field induced gap, also stemfrom the ability or inability of the samples to carry boundarycurrents under the specific experimental conditions.

IV. CONCLUSIONS

In summary, a ZBCP field splitting is observed in tunneljunctions fabricated on optimally doped~100!- and ~110!-oriented films. The ZBCP splits as a function of magneticfield with a hysteresis which is thickness dependent, i.e., thehysteresis increases with the film thickness. The splitting isgenerally weaker in~100!-oriented films, particularly in de-

creasing fields where it is negligible. In~110!-oriented films,splitting is strong even in decreasing fields, where it is foundto be thickness independent and to have a square root depen-dence on magnetic field for fields ranging from 0 to 16 T. Weattribute the hysteretic behavior to the Doppler shift effectpredicted by Fogelstromet al.,13 and the splitting in decreas-ing fields to node removal. Our data in decreasing fields forwhich Meissner currents are negligible are in good agree-ment with the existence of a field inducedidxy componentpredicted by Laughlin.8 His theory, however, does not takeinto account the orientation of the samples boundaries, whichwe find to be crucial. We conjecture that the presence of~110! surfaces on opposite faces of the sample is necessaryfor the flow of Laughlin’s currents, and thus for the estab-lishment of theidxy order parameter. Furthermore, his modeldoes not take into account the presence of vortices, aspointed out by Liet al.27 More theoretical work is necessaryto establish whether Laughlin’s model can explain the effectof films orientation on the field-splitting of the zero biasconductance peak.

ACKNOWLEDGMENTS

We are indebted to Malcom Beasley for pointing out toone of us~G.D.! Ref. 20 on the effects of Bean-Livingstonbarrier as seen in a tunneling experiment, and to Dr. H. Cas-tro and A. Kohen for helpful conversations. This work wassupported by the Heinrich Herz-Minerva Center for HighTemperature Superconductivity, by the Israel Science Foun-dation and by the Oren Family Chair of Experimental SolidState Physics.

*Email address: [email protected], Home page:www.tau.ac.il\;supercon

†Present address: Center for Superconductivity Research, Depart-ment of Physics, University of Maryland College Park, CollegePark, Maryland 20742, USA.1Y. Tanuma, Y. Tanaka, and S. Kashiwaya, Phys. Rev. B64,

214519~2001!.2A. V. Balatsky, M. I. Salkola, and A. Rosengren, Phys. Rev. B51,

15547~1995!.3Y. Ohashi, J. Phys. Soc. Jpn.65, 823 ~1996!.4A. Kohen, G. Leibovitch, and G. Deutscher, Phys. Rev. Lett.90,

207005~2003!.5A. V. Balatsky, Phys. Rev. B61, 6940~2000!.6Y. Dagan and G. Deutscher, Phys. Rev. Lett.87, 177004~2001!.7M. Vojta, Y. Zhang, and S. Sachdev, Phys. Rev. Lett.85, 494

~2000!.8R. B. Laughlin, Phys. Rev. Lett.80, 5188~1988!.9K. Krishana, N. P. Ong, Q. Li, G. D. Gu, and N. Koshizuka,

Science277, 83 ~1997!.10A. Aubin and K. Behnia, Science280, 9a ~1998!.11G. Deutscher, Y. Dagan, A. Kohen, and R. Krupke, Physica C

341–348, 1629~2000!.12C. R. Hu, Phys. Rev. Lett.72, 1526~1994!.13M. Fogelstrom, D. Rainer, and J. A. Sauls, Phys. Rev. Lett.79,

281 ~1997!.

14M. Covington, M. Aprili, E. Paraoanu, L. H. Greene, F. Xu, J.Zhu, and C. A. Mirkin, Phys. Rev. Lett.79, 277 ~1997!.

15J. R. Clem,Thirteenth International Conference on Low Tempera-ture, Boulder, Colorado, 1972, edited by K. D. Timmerhaus~Plenum Press, New York, 1974!, p. 102.

16Y. Dagan, R. Krupke, and G. Deutscher, Europhys. Lett.51, 116~2000!.

17R. Krupke and G. Deutscher, Phys. Rev. Lett.83, 4634~1999!.18Y. Dagan, R. Krupke, and G. Deutscher, Phys. Rev. B62, 146

~2000!.19J. F. Bussiere, Phys. Lett.58A, 343 ~1976!.20D. F. Moore and M. R. Beasley, Appl. Phys. Lett.30, 494~1977!.21M. Xu, D. K. Finnemore, G. W. Crabtree, V. M. Vinokur, B.

Dabrowski, D. G. Hinks, and K. Zhang, Phys. Rev. B48, 10630~1993!.

22M. Aprili, E. Badica, and L. H. Greene, Phys. Rev. Lett.83, 4630~1999!.

23J. Lesueur, L. H. Greene, W. L. Feldmann, and A. Inam, PhysicaC 191, 325 ~1992!.

24A. Sharoni, O. Millo, A. Kohen, Y. Dagan, R. Beck, G. Deutscher,and G. Koren, Phys. Rev. B65, 134526~2002!.

25L. Alff, Eur. Phys. J. B5, 423 ~1998!.26H. Aubin and L. H. Greene, Phys. Rev. Lett.89, 177001~2002!.27Mei-Rong Li, P.J. Hirschfeld, and P. Wo¨lfe, Phys. Rev. B63,

054504~2001!.

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Chapter 6

Determination of the criticalcurrent by nodal tunnelling

In this paper [20], we show that, by measuring the tunneling conductance in (110)

films under applied magnetic fields, it is possible to calculate the Bean critical current

density.

We measured the difference between the Zero Bias Conductance Peak (ZBCP)

splitting in decreasing fields and a field-cooled configuration. We found, that this

difference, for a given field, can be correlated to the Bean critical current density, via

the Doppler shift effect.

Such a none destructive technique for measuring the critical current density could

be useful for applications since it avoids having to make high current contacts with

the sample.

The full reference of the paper is: Beck, R., Leibovitch, G., A. Milner, A. Gerber.,

and Deutscher, G. (2004) Superconducting science and technology 17, 1069.

55

56 Determination of the critical current by nodal tunnelling

INSTITUTE OF PHYSICS PUBLISHING SUPERCONDUCTOR SCIENCE AND TECHNOLOGY

Supercond. Sci. Technol. 17 (2004) 1069–1071 PII: S0953-2048(04)79306-9

Determination of the critical currentdensity in the d-wave superconductorYBCO under applied magnetic fields bynodal tunnelling

Roy Beck, Guy Leibovitch, Alexander Milner, Alexander Gerberand Guy Deutscher

School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences,Tel-Aviv University, 69978 Tel-Aviv, Israel

Received 4 April 2004Published 18 June 2004Online at stacks.iop.org/SUST/17/1069doi:10.1088/0953-2048/17/8/022

AbstractWe have studied nodal tunnelling into YBa2Cu3O7−x (YBCO) films undermagnetic fields. The films’ orientation was such that the CuO2 planes wereperpendicular to the surface with the a and b axis at 45 from the normal.The magnetic field was applied parallel to the surface and perpendicular tothe CuO2 planes. The zero bias conductance peak (ZBCP) characteristic ofnodal tunnelling splits under the effect of surface currents produced by theapplied fields. Measuring this splitting under different field conditions, zerofield cooled and field cooled, reveals that these currents have differentorigins. By comparing the field cooled ZBCP splitting to that taken indecreasing fields we deduce a value of the Bean critical current superfluidvelocity, and calculate a Bean critical current density of up to3 × 107 A cm−2 at low temperatures. This tunnelling method for thedetermination of critical currents under magnetic fields has seriousadvantages over the conventional one, as it avoids having to make highcurrent contacts to the sample.

As shown by de Gennes and Saint James [1], finite energybound states are formed in a normal metal film (N) in contactwith a conventional (s-wave symmetry) superconductor (S).These states have energies smaller than the gap in S. Theycorrespond to Saint James cycles [2], in which an electron isconverted at the N/S interface into a reflected hole [3], whichundergoes a specular reflection at the outer surface of N beforebeing Andreev reflected into an electron at the interface, andfinally specularly reflected, thus completing the cycle. SimilarSaint James cycles occur when S is a d-wave superconductor,but with one major difference. As shown by Hu [4], if theinterface is perpendicular to a nodal direction, zero energybound states are formed because of the phase difference of π

between successive Andreev reflections. These zero energystates persist in the limit where the normal metal thicknessis zero. They produce the ZBCP in the nodal tunnellingconductance [5].

As shown by Fogelstrom et al [6], surface currents flowingin the CuO2 planes break time reversal symmetry and induce aDoppler shift (DS) of the zero energy states, resulting in a splitof the ZBCP. Such currents can be Meissner’s origin generatedby a magnetic field applied parallel to the surface (after zerofield cooling of the sample), as in [7] and [8]. Meissnercurrents increase at first linearly with field, and eventuallyup to fields of the order of the thermodynamical field Hc ifthe Bean–Livingston barrier [9] is effective, and so shouldthe splitting given by δ↑(H) = vS pF sin , where vS is thesuperfluid velocity of the Bean–Livingston currents, pF theFermi momentum of tunnelling particles and the width ofthe tunnelling cone. This linear behaviour has been observedexperimentally [7, 8, 10]. Moreover, as shown by Krupke andDeutscher [10] and by Aprili et al [11], splitting does not occurwhen the field is applied parallel to the CuO2 planes, which isa strong indication that the ZBCP is indeed due to the d-wavesymmetry.

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57

R Beck et al

100 5 150

1

2

3

4

5

δ (

mV

)

µ0H(Tesla)

Figure 1. ZBCP splitting, δ, as a function of magnetic field appliedparallel to the film surface and perpendicular to the CuO2 planes at0.3 K. The circles indicate measured splitting in field cooledconditions, and triangles zero field cooling with increasing (pointingup) and decreasing (pointing down) fields in the range of 0–16 T.

The correlation between surface currents and splitting ofthe ZBCP having been previously established experimentallyunder conditions of increasing fields, we show here how itis possible from splitting measurements to determine surfacecurrent densities under different conditions. Specifically,the difference between splitting values measured under fieldcooled (FC) and decreasing field conditions gives access to theBean critical current density. We find that at 4.2 K it does notvary significantly in YBCO films up to fields of 15 T, remainingequal to about 3 × 107 A cm−2.

1. Experimental details

We have formed tunnelling junctions by pressing an indiumwire on a fresh film of off-axis sputtered Y1Ba2Cu3O7−x asdescribed elsewhere [12]. The films’ thicknesses were 1600and 3200 Å, with a Tc of 89 ± 2 K. The films were in-plane oriented, with the [0, 0, 1] axis oriented parallel to oneof the film’s edges, and the [1, 1, 0] axis oriented parallelto the other one. The crystallographic direction normal tothe surface, in which the tunnel junction was directed, was[1, 1, 0], as verified by x-ray diffraction. Scanning electronmicroscopy and atomic force microscopy of the films surfacerevealed well oriented crystallites, with a surface roughnessof a few nanometres. We have measured I/V curves usinga DC current supply and a digital voltmeter, and calculatedthe differential conductance (i.e. dI/dV versus V ) numericallywithout any data manipulation such as averaging of the readoutdata. The junctions’ quality was verified by observing theindium superconducting gap feature at zero magnetic field atT < Tc of the indium (3.4 K). The magnetic field was appliedparallel to the film’s surface and along the c-axis direction,perpendicular to the CuO2 planes.

2. Results and discussion

Figure 1 shows splitting values of the ZBCP measured underFC conditions, together with values taken in zero FC inincreasing and decreasing fields for a 1600 Å thick sample at0.3 K. The FC values are smaller than those taken in increasing

0 1 2 3 40

1

2

3

4

5

δ (

mV

)

(µ0H)1/2(Tesla1/2)

Figure 2. ZBCP splitting, δ, as a function of the square root of theapplied magnetic field, for field cooled conditions (stars) anddecreasing field conditions (circles). Linear fits to the data (lines)have slopes 1.14 ± 0.03 and 1.16 ± 0.02 mV T−1/2 and intersectionsof 0.66 ± 0.09 and 0.03 ± 0.02 mV for field cooled and decreasingfield respectively.

(This figure is in colour only in the electronic version)

fields, and larger than those taken in decreasing ones, beingcloser to the latter. This order can be understood if we assumethe existence of a field-induced imaginary component of theorder parameter, possibly having idx y symmetry as argued byBeck et al [12]. Such a component induces a splitting equalto its amplitude. In increasing fields, the splitting is enhancedby the additional contribution of the Doppler shift generatedby the Bean–Livingston (BL) currents as discussed above. Inaddition, there may also be a contribution of the Bean criticalstate currents due to bulk pinning, usually weaker than thatof the BL currents and flowing in the same direction. UnderFC conditions, there are neither BL nor Bean currents; thedominant contribution to the splitting is that of the imaginarycomponent. Under decreasing fields, there are no BL currents(there is no BL barrier against flux exit), but there will bereversed Bean currents. The difference between the FC and thedecreasing field data is then due to the Bean surface currents.

We show in figure 2 the FC data as a function of H1/2.It is similar to that of data taken in decreasing fields, alsoshown. Both sets of data can be fitted to straight lineshaving a slope of 1.1 mV T−1/2, in agreement with Beck et al

[12]. The origin of this field dependence has been discussedelsewhere [12]. Briefly, it has been attributed to a field-induced idx y component of the order parameter, as originallyproposed by Laughlin [13]. Actually, under FC conditions,an additional contribution comes from the finite equilibriumscreening currents corresponding to the bulk magnetization.These currents are of the order of the difference between theinduction and the applied field, divided by the distance from thesurface to the first vortices, itself of the order of the intervortexdistance [14]. In decreasing fields, the Bean critical statecurrents run in a direction opposite to that of the equilibriumcurrents, thus reducing the splitting. What we wish to exploithere is the difference between the two sets of data. Sincethey fit parallel lines, the Bean critical current must be fieldindependent in the range of fields investigated. We have foundthat the constant difference between the two lines is about0.6 mV for that 1600 Å thick sample. We can use this value to

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58 Determination of the critical current by nodal tunnelling

Determination of the critical current density in the d-wave superconductor YBCO under applied magnetic fields by nodal tunnelling

calculate the velocity of the Bean currents using the expressiongiven by Fogelstrom et al [6]:

δFC − δ↓ = vS(B)pF sin (1)

where δFC and δ↓ are the splitting in FC and in decreasing fieldrespectively, and vS(B) is now the superfluid velocity of the

Bean critical state currents, rather than that of the BL currentsas in [6]. Taking the wavevector of the Fermi surface to bekF = 1 × 108 cm−1, and estimating the tunnelling cone to be = 20, we calculate vS = 2.7 × 104 cm s−1. Then, fromjc = nevS, with a superfluid density, n = 5 × 1021 cm−3, weobtain for the critical current density jc = 2.2×107 A cm−2 at0.3 K. For a somewhat thicker sample (3200 Å), the differencebetween the FC and decreasing fields data is 0.9 meV, and weobtain jc = 3×107 A cm−2 at 4.2 K. These values are in goodagreement with direct measurements [15]. It turns out that theBean currents are of the same order as that of the calculatedequilibrium screening currents under field cooled conditions(but of course of opposite direction). This may explain whythe straight line running through the decreasing field splittingdata in figure 2 extrapolates closer to zero at zero field than theFC data does.

3. Conclusions

We have measured the nodal tunnelling conductance intoYBCO films under magnetic fields applied parallel to thesurface and perpendicular to the CuO2 planes. We haveshown that the Bean critical current density can be obtainedby taking the difference in the splitting of the zero biasconductance peak, in a given magnetic field, between FC anddecreasing field data. We have found this critical currentto be field independent and equal to about 3 × 107 A cm−2

up to 16 T at low temperatures. This novel method avoids

having to pattern the sample, thus removing the difficultiesassociated with possible heating effects under strong injectedcurrents.

Acknowledgments

We are indebted to Roman Mints and Vladimir Koganfor an enlightening discussion on the field dependence ofscreening currents under field cooled conditions. This workwas supported by the Heinrich Hertz Minerva Center forHigh Temperature Superconductivity, by the Israel ScienceFoundation and by the Oren Family Chair for ExperimentalSolid State Physics.

References

[1] De Gennes P G and Saint James D 1963 Phys. Lett. 4 151[2] Saint James D 1964 J. Physique 25 899[3] Andreev A F 1964 Sov. Phys.—JETP 19 1228[4] Hu C R 1994 Phys. Rev. Lett. 72 1526[5] Kashiwaya S et al 1995 Phys. Rev. B 51 1350[6] Fogelstrom M, Rainer D and Sauls J A 1997 Phys. Rev. Lett.

79 281[7] Lesueur J, Greene L H, Feldmann W L and Inam I 1992

Physica C 191 325[8] Covington M, Aprili M, Paraonu E, Greene L H, Xu F,

Zhu J and Mirkin C A 1997 Phys. Rev. Lett. 79 277[9] Bean C P and Livingston J D 1968 Phys. Rev. Lett. 12 14

[10] Krupke R and Deutscher G 1999 Phys. Rev. Lett. 83 4634[11] Aprili M, Badica E and Greene L H 1999 Phys. Rev. Lett. 83

4630[12] Beck R, Dagan Y, Milner A, Gerber A and Deutscher G 2004

Phys. Rev. B 69 144506[13] Laughlin R B 1998 Phys. Rev. Lett. 80 5188[14] Clem J R 1974 13th Int. Conf. on Low Temperature (Boulder,

CO, 1972) vol 102, ed K D Timmerhaus (New York:Plenum)

[15] Senoussi S 1992 J. Physique III 2 1041

1071

Chapter 7

Transition in the tunnelingconductance in high magnetic fields

In the following two papers [19, 41] we study the tunneling density of states under ap-

plied fields up to 32.4T. These studies focus on measurements on the superconducting

gap energy scale.

We observe that, under strongly induced nodal currents, an interesting transition

in the tunneling conductance occurs. In high fields, the gap-like feature shifts dis-

continuously from 15 meV to a lower bias of 11 meV, and becomes more pronounced

as the field increases. The effect takes place around 9 T in increasing fields and the

transition back to the initial state occurs at around 5 T in decreasing fields. We

discussed the possible origins for the effect in terms of current and/or field effect.

The full reference of the papers are:

Beck, R., Dagan, Y., Milner, A., Leibovitch, G., Gerber, A., Mints, R. G., and

Deutscher, G. (2005) Phys. Rev. B 72(10), 104505.

Beck, R., Dagan, Y., Leibovitch, G., Elhalel, G., and Deutscher, G. (2005) AIP Conf.

Proc. Ser. (in press).

59

60 Transition in the tunneling conductance in high magnetic fields

Transition in the tunneling conductance of YBa2Cu3O7− films in magnetic fields up to 32.4 T

R. Beck,1,* Y. Dagan,1,2 A. Milner,1,† G. Leibovitch,1 A. Gerber,1 R. G. Mints,1 and G. Deutscher1

1School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Science, Tel-Aviv University, 69978 Tel-Aviv, Israel2Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, Maryland 20742, USA

Received 28 April 2005; published 9 September 2005

We studied the tunneling density of states in YBa2Cu3O7− films under strong currents flowing along nodedirections. The currents were induced by fields of up to 32.4 T parallel to the film surface and perpendicular tothe CuO2 planes. We observed an interesting transition in the tunneling conductance at high fields where thegaplike feature shifts discontinuously from 15 meV to a lower bias of 11 meV, becoming more pronounced asthe field increases. The effect takes place in increasing fields around 9 T and the transition back to the initialstate occurs around 5 T in decreasing fields.

DOI: 10.1103/PhysRevB.72.104505 PACS numbers: 74.72.Bk, 74.25.Ha, 74.50.r, 74.78.w

I. INTRODUCTION

The order parameter of a d-wave superconductor has nodelines located at angles ±= ± /4, where is the angle be-tween the quasiparticle momentum and the crystallographic1,0,0 direction.1 As a result, the tunneling density of statesof a d-wave superconductor is significantly different fromthat of a conventional s-wave superconductor. In particular, itreveals the existence of low energy surface bound states,which are the origin of the zero bias conductance peak at pairbreaking surfaces.2,3 The high conductance at low bias, be-low the d-wave gap, is in sharp contrast with the low con-ductance in an s-wave superconductor at similar bias. Thed-wave gap itself is marked in the tunneling density of statesby a weak structure called the gaplike feature3 see Fig. 1.The zero bias conductance peak and gaplike featureare well identified in the tunneling density of states of high-Tc cuprates4,5 and simultaneously observed when the surf-ace roughness scale is smaller than the junction size.5,6 Itwas predicted that a d-wave symmetry can be modified by aperturbation that creates a gradient of the order parameter.This is the case of a vortex core,7 sample surface,8 andcurrents.9,10

In this study we report measurements of the conductivityof In/YBa2Cu3O7− YBCO junctions. Currents in theYBCO film are induced by applying magnetic fields, parallelto the surface and perpendicular to the CuO2 planes. Filmshaving 110 and 100 orientation are used, respectively, toinduce nodal and antinodal currents.

The tunneling conductance changes remarkably for the110 films in high magnetic fields-high currents in a domainthat has not been investigated until now. The position of thegaplike feature shifts down discontinuously in increasingfields around 9 T and in decreasing fields around 5 T. Weargue that these shifts are due to nodal surface currents in-duced by the applied field, with the field itself, possibly in-ducing a certain modification of the vortex state. No transi-tion is observed when the field is parallel to the CuO2 planesFig. 1b or when the film has the 100 orientation Fig.1c. In both cases there are no currents flowing along thenodal direction.

FIG. 1. Color online dI /dV vs bias voltage; magnetic fieldapplied parallel to the films surface up to 16 T at 4.2 K. a A 110in-plane orientated film at increasing field. The field is perpendicu-lar to the CuO2 planes sample 1. b A 110 in-plane orientatedfilm at increasing field. The field is parallel to the CuO2 planessample 1. c A 100 in-plane orientated film. The field is perpen-dicular to the CuO2 planes. Solid dashed arrows indicate the ga-plike feature positions at low high fields. A remarkable change inthe spectrum is observed at high fields only when the field is per-pendicular to the CuO2 planes and the nodal direction is normal tothe film surface.

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61

II. EXPERIMENTAL RESULTS

Our oriented films were sputtered onto 110 SrTiO3 and100 LaSrGaO4. All films have a critical temperature of89 K slightly underdoped. Tunneling junctions were pre-pared by pressing a freshly cut indium pad onto the films’surface.12 These junctions are of high quality, as shown bytheir low zero-bias conductances below the critical tempera-ture of the indium electrodes.12 A schematic drawing of thecrystallographic orientation and experimental setup is shownin Fig. 2.

Tunneling characteristics in 110 films at zero magneticfield exhibit the known zero-bias conductance peak andgaplike feature Fig. 1a. The magnetic field splitting ofthe zero-bias conductance peak was previously ad-dressed.4–6,12–14 We focus here on the field dependence of thegaplike feature at high bias. It shows a progressive, roughlylinear, shift of the peak position from 17 to 15 meV as thefield increases from 0 to 1 T. This initial decrease is fol-lowed by a flat region up to 6 T. If that field is not exceedand then reversed a hysteresis loop is described ending upwith a flat region at low field. If the field is increased above6 T the gaplike feature amplitude starts to shrink until, at8 T, it cannot be identified anymore. In the range of 8–11 Ta flat maximum develops between 10 and 15 meV. An11 meV peak builds up with the field and is clearly identifiedabove 11 T. Up to a field of 16 T, no detectable smearing ofthis peak occurs.

Reducing the field from values larger than 11 T has an-other interesting effect. The 11 meV peak gradually shiftsback to 14 meV as the field is reduced by about 1 T, forexample from 15 to 14 T Fig. 3 or from 32.4 to 31.5 TFig. 4b. In contrast to the 9 T field up transition, the shiftback to 14 meV is continuous, which shows that the newpeak at 11 meV is indeed a new gaplike feature rather thanbeing related for instance to the split zero-bias conductancepeak. By further reducing the field, the 14 meV peak shrinkswhile the 16 meV builds up below 5 T Fig. 5a. An analo-gous behavior is seen under field cooled conditions Fig.5b.

The overall variation of the gaplike feature peak positionwith respect to the applied field can be seen in Fig. 3. Thejump in its position can be clearly observed in increasingfields above 8 T and decreasing fields lower than 6 T. Thegradual increase of the 11 meV peak amplitude as the field isincreased beyond 10 T Fig. 6 suggests that it characterizesa different superconducting state.

FIG. 2. Color online Schematic presentation of the measure-ment setup for the 110 films. Indium pads are pressed against thesurface of the oriented thin film. The orientation of the film enablesus to apply a magnetic field parallel or perpendicular to the CuO2

layers while the field is kept parallel to the films’ surface and per-pendicular to the tunneling current.

FIG. 3. Color online Gaplike feature position for sample 1 inincreasing and decreasing magnetic fields at 4.2 K. Datataken both for positive full and negative hollow field polarity.Black red represent the low high field state.

FIG. 4. Color online a dIdV vs bias voltage for sample 2measured at 1.3 K in increasing magnetic fields. b Gaplike featureposition in increasing and decreasing fields.

FIG. 5. Color online dI /dV vs bias voltage for sample 3 mea-sured at 0.5 K. a Decreasing fields from 16 T. b Field cooledconditions. Note that the intermediate field peak conductance islower than both the high and low field ones.

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III. DISCUSSION

The rapid change in the peak position upon field reversalFigs. 3 and 4b means that its position is affected by fieldinduced currents. The strong difference between 100 and110 oriented films, both showing a similar gaplike feature,presumably due to surface roughness,6 indicates that thesecurrents flow over a depth much larger than the surfaceroughness a few tens of nanometers.

The Bean-Livingston barrier15 can prevent the entry ofvortices up to fields of the order of the thermodynamicalcritical field, Hc 1 T for YBCO. The rapid initial de-crease of the gaplike feature peak position from 16 meVdown to 14 meV over that field range can be due to thedelayed vortex entrance see Fig. 3. We name the corre-sponding currents surface vortex currents, jV. This is con-firmed by the low field hysteresis loop, as there is no Bean-Livingston barrier in decreasing fields. This initial decreaseis not observed in 100 oriented films where the currents atthe surface flow along an antinodal direction. This decreaseis therefore clearly due to nodal currents. The major questionraised here concerns however the origin of the 11 meV peakseen in increasing fields above 10 T. It could be a currenteffect, or a field effect, or a combination of both.

In addition to the vortex surface currents, jV, one shouldalso consider. The Meissner screening current, jM, and theBean current jB due to vortices pinned in the bulk. Weshowed14 that by measuring the difference between fieldcooled and decreasing field splitting values of the zero-biasconductance peak also due to the surface currents6, one canestimate the Bean critical current value. We found that jB isroughly constant up to fields of 16 T and has a value of a fewtens of MA/cm2.

The surface current can be obtained by calculating thedepth, d, of the vortex-core free area at the sample surface.15

Its derivation is not affected by the d-wave symmetry andhas to include the Bean current jB. In the following the effectof the vortex surface current is neglected. Consider a semi-infinite superconductor in a uniform magnetic field H. Thefield inside, bx, is the solution of London’s equation which

has to match the boundary conditions b0=H, bd= B and

the vortex matter equilibrium condition jd= jB, where B is

the local induction value. In the field range Hc1HHc2 wehave d and jB jM:

d 2H − B/H + 4jB

2/cH , 1

where is London’s penetration depth. The same approxi-

mation results in BB, where B is the equilibrium induc-tion, j jMH+ jB in increasing fields and j jMH− jB indecreasing fields, where

jM =c

4

− 8HM =c

420H

4ln

Hc2

H, 2

and 0 is the flux quantum. We find jM 2.2108 A/cm2

for H=90 kOe, =1500 Å, and Hc2=1200 kOe.We emphasize that the contributions of jV, jM, and jB may

all be important for the interpretation of the experiment. Thefield reversal effect can be explained by jB and/or jV. Afterfield reversal, jB changes sign while jV is negligible.15

We note that the progressive enhancement of the 11 meVpeak in increasing fields Fig. 6 suggests a transition to adifferent superconducting state. Any continuous reduction ofthe d-wave gap would not be accompanied by an enhance-ment of its gaplike feature peak amplitude.

The superconducting phase could be a different vortexstate,17 in such case the transition would be basically fieldinduced. Alternatively, the new phase could appear due tostrong nodal currents and possibly have an order parameterwith a symmetry different from a pure d wave.9,10

A general difficulty in comparing our data to existingtheories is that they have addressed only the small currentlimit.9–11 We can only offer some speculations as to what ahigh current phase might be. In a previous publication13 wediscussed the zero-bias conductance peak field splitting interms of a field-induced idxy component. But we have foundno correlation between the zero-bias conduction peak split-ting and the gaplike feature position implying that their ori-gins are different. For instance, after decreasing the fieldfrom 16 to 15 T, the position of the gaplike feature remainsunchanged down to 5 T see Fig. 3, but the zero-bias con-ductance peak splitting reduce from 4.2 to 2.5 meV see Fig.4 in Ref. 13. We speculate that surface currents on the co-herence length scale could split the zero-bias peak,6 but, asshown here, only currents on much larger length scale areaffecting the position of the gaplike feature position.

The fact that we observe a regime where two gap featurescoexist, both in increasing and decreasing fields as well as infield cooled conditions, with a definite hysteresis, suggests afirst order transition showing superheating and supercoolingeffects. To be specific, following the position and amplitudeof the gaplike feature as a function of applied field we ob-served that the transition from low to high fields state takesplace at 9 T superheating and back from the high to lowfields at 5 T supercooling.

The effect of reducing the low-lying density of states isindependent on the high current-high field phase nature. Asshown in Fig. 4a, this is well beyond the field-current re-gion where the zero-bias conductance peak vanished. A tran-sition to an inhomogeneous state in the case of nodal cur-rents was recently speculated about by Khavkine et al.9 We

FIG. 6. 11 meV gaplike feature peak amplitude of sample 2 forincreasing fields. The enhancement up to 20 T suggests that thehigh fields state has a stronger coherence peak.

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63

also note that in very high fields the vortices nearest to thesurface are located within a few coherence lengths, whichmay affect the tunneling conductance.16

A different explanation to the data would be that the re-markable transition in the tunneling conductance at 9 T inincreasing fields is a vortex state transition, e.g., Bragg tovortex glass.18 Such a transition is known to be irreversibleas observed. The vortex state could modify the pinning and,hence, the total nodal current or its’ effect on the order pa-rameter. This could explain the large hysteresis observed athigh fields. However, in contradiction to the high bias region,the low bias region which is also sensitive to total current viathe Doppler shift mechanism,6 does not show substantialhysteresis.

IV. SUMMARY

In conclusion, we have observed a transition in the tun-neling conductance in high magnetic fields in YBCO 110oriented films. A transition of the gaplike feature positionand amplitude is present in both increasing and decreasingfields and under field cooled conditions for fields orientedparallel to the surface and perpendicular to the CuO2 planesin such a way as to induce currents along nodal directions.

We have proposed that the observed transition may be in-duced by these currents. In the high current state, the densityof low energy states is reduced, possibly indicating the emer-gence of a component of the order parameter leading towardsa fully gaped state. Alternatively, the changes in the tunnel-ing characteristics may be due to a transition between twovortex states, having different gap values and sensitivity tonodal currents.

ACKNOWLEDGMENTS

This work was supported by the Heinrich Herz-MinervaCenter for High Temperature Superconductivity, the IsraelScience Foundation, the Oren Family Chair of ExperimentalSolid State Physics, and NSF Grant No. 0352735. Work car-ried out at the National High Magnetic Field Laboratory atTallahassee is supported by an NSF cooperative agreementNo. DMR-00-84173 and the State of Florida. The work ofR.M. was supported in part by Grant No. 2000011 from theUnited States-Israel Binational Science Foundation BSF,Jerusalem, Israel. G.D. is indebted to Philippe Nozieres forvery helpful discussions. We are indebted to Amlan BiswasUF for his contribution to the NHMFL experiment and toAmir Kohen for discussions.

*Electronic address: [email protected]†Present address: Department of Chemical Physics, Weizmann In-

stitute of Science, Rehovot 76100, Israel.1 C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys. 72, 969 2000; D.

J. Van Harlingen, Rev. Mod. Phys. 67, 515 1995.2 C.-R. Hu, Phys. Rev. Lett. 72, 1526 1994.3 S. Kashiwaya, Y. Tanaka, M. Koyanagi, H. Takashima, and K.

Kajimura, Phys. Rev. B 51, 1350 1995.4 M. Covington, M. Aprili, E. Paraoanu, L. H. Greene, F. Xu, J.

Zhu, and C. A. Mirkin, Phys. Rev. Lett. 79, 277 1997; M.Aprili, E. Badica, and L. H. Greene, Phys. Rev. Lett. 83, 46301999.

5 Y. Dagan and G. Deutscher, Phys. Rev. Lett. 87, 177004 2001.6 M. Fogelström, D. Rainer, and J. A. Sauls, Phys. Rev. Lett. 79,

281 1997.7 M. Franz, D. E. Sheehy, and Z. Tesanovic, Phys. Rev. Lett. 88,

257005 2002.8 Y. Tanuma, Y. Tanaka, and S. Kashiwaya, Phys. Rev. B 64,

214519 2001.9 I. Khavkine, H.-Y. Kee, and K. Maki, Phys. Rev. B 70, 184521

2004.

10 M. Zapotocky, D. L. Maslov, and P. M. Goldbart, Phys. Rev. B55, 6599 1997; V. V. Kabanov, Phys. Rev. B 69, 0525032004.

11 D. Xu, S. K. Yip, and J. Sauls, Phys. Rev. B 51, 16233 1995.12 Y. Dagan, R. Krupke, and G. Deutscher, Europhys. Lett. 51, 116

2000.13 R. Beck, Y. Dagan, A. Milner, A. Gerber, and G. Deutscher,

Phys. Rev. B 69, 144506 2004.14 R. Beck, G. Leibovitch, A. Milner, A. Gerber, and G. Deutscher,

Supercond. Sci. Technol. 17, 1069 2004.15 J. R. Clem, in Proceeding of 13th International Conference on

Low Temperature Physics Boulder, Colorado, 1972, edited by K.D. Timmerhaus, W. J. O’Sullivan, and E. F. Hammel PlenumPress, New York, 1974.

16 S. Graser, C. Iniotakis, T. Dahm, and N. Schopohl, Phys. Rev.Lett. 93, 247001 2004.

17 J. Shiraishi, M. Kohmoto, and K. Maki, Phys. Rev. B 59, 44971999.

18 Y. Radzyner, A. Sheulov, and Y. Yeshurun, Phys. Rev. B 65,100513R 2002.

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Tunneling into YBCO Superconductor at High Magnetic Field

R. Becka, Y. Dagana,b, G. Leibovitcha, G. Elhalela and G. Deutschera

a School of Physics and Astronomy, Faculty of Exact Science, Tel-Aviv University, 69978, Tel-Aviv, Israel b Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, Maryland 20742, USA

Abstract. We studied the tunneling density of states of YBCO films at high magnetic field up to 15 Tesla parallel to the films’ surface and perpendicular to the CuO2 planes. We observed a transition in the tunneling conductance at high fields. At 6 Tesla in increasing magnetic fields, the gap-like feature shifts discontinuously from 15meV to a lower bias of 11meV, and becoming more pronounced as the field increases. We found the effect to be anisotropic. We discuss its origin in term of current and/or magnetic field.

Keywords: Tunneling, High magnetic field, Superconductivity, YBCO thin films. PACS: 74.50.+r, 74.25.Ha

INTRODUCTION

Tunneling into a d-wave superconductor is far richer than into a conventional superconductor. Hu1 predicted that tunneling along the node direction will result in zero energy bound states, resulting from the phase difference at adjacent lobes. Modification of the phases, for example by a supercurrent parallel to sur-face, will result in a splitting of the zero bias peak, proportional to the superfluid velocity2. Moreover, even in nodal directed tunneling, when the junction size exceeds the roughness of the films’ surface2, one can also measure the superconducting gap value as it appears as an additional peak in tunneling differential conductance near the gap value.

We investigate the tunneling conductance of In/insulator/YBCO junctions when a magnetic field is applied parallel to the film and perpendicular to the CuO2 planes. We observe that for slightly underdoped samples the gap-like feature shifts discontinuously at about 6 Tesla in increasing magnetic field. We discuss the origin of the shift in terms of current and/or field.

EXPERIMENT

We measure the tunneling conductance of slightly underdoped thin films of YBa2Cu3O7- oriented along the node direction. The crystallographic orientation of the films is shown in Fig 1a. The advantage of this configuration is that it enables one to apply magnetic fields perpendicular or parallel to the CuO2 plains

while keeping the field parallel to the surface. Forming a planar tunneling junction perpendicular to the film's surface allows studying the influence of the magnetic field on the superconductor with little influence of vortices. A detailed description of the films prepara-tion and junction configuration can be found in refer-ence3.

FIGURE 1. Differential conductance of the tun-neling junction at 2.5K in increasing magnetic fields. a) Illustration of the film crystallographic orientation and experimental configuration. b) Gap-like feature bias value in increasing (

) and decreasing ( ) fields.

A typical tunneling spectrum is shown in Fig 1. At zero magnetic field the zero-bias peak and the gap-like feature, located at 16.3 meV, are clearly shown. Fol-lowing the evolution of the tunneling spectrum with

65

increasing magnetic field, reveals two opposite be-haviors. While the zero bias peak is continually split-ting with magnetic field, the gap feature reverses its trend at some point. At low fields the gap-like feature is slightly reduced down to 15 meV, until at 6 Tesla it can not be detected any more. Further increasing the magnetic field results in the appearance of a new gap-like feature, at 11 meV, whose amplitude grows with increasing magnetic fields. Next we decrease the mag-netic field, we note that by reducing it from 14 to 13 Tesla the position of the gap-like feature shifts con-tinuously from 11 to 14 meV [see also Ref. 4]. The bias values of the gap-like feature in both, increasing and decreasing fields, present the hysteretic behavior shown in Fig. 1b. This effect is highly reproducible, and can be measured up to 25K.

We repeated the experiment with films having dif-ferent crystallographic orientations. In particular, films oriented with the a-axis perpendicular to the surface and the c-axis parallel to the film surface, and the magnetic field parallel to the c-axis as before. In such case, the gap-like feature is hardly modified with fields up to 15 Tesla. The same holds for the magnetic field applied parallel to the CuO2 planes for any crystallo-graphic configuration.

DISCUSSION AND CONCLUSIONS

From the hysteretic behavior of the gap-like feature we deduce that the bias value is strongly affected by induced currents rather than by the field itself. We notice that the gap-like feature is continuously shifting when reducing the field from its maximum value by 1T. Hence, we infer that the gap-like feature at 11 meV is indeed the successor of the zero field gap-like feature.

A possible explanation for the discontinuous shift at 6 Tesla could be a sudden change in the induced current, for example due to a phase transition in the vortex matter5. However, the low bias region is highly sensitive to the surface currents, via the Doppler shift effect on the Andreev-Saint-James bound states2. Therefore, one would expect to see the same evidence for the discontinuous shift in the low bias region as well. But, as shown in the contour plot in Fig 2, the low bias region is continuous over the whole range of magnetic field, in contrast to the high bias region, were states are shifted abruptly to the region of the new gap-like feature.

An alternative origin for the discontinuous shift is the magnetic field alone. However, in such a case the modification of the gap-like feature with field should

be present in a-axis films as well, which is inconsistent with our measurements.

Therefore, with no other alternative, we conclude that the anisotropic discontinuous shift taking place at 6 Tesla is the result of a combination of strong currents and high magnetic field. To the best of our knowledge, no theoretical model has predicted such effect.

0 5 10 15 200

4

8

12

Bias (mV)

0H (

Te

sla)

No

rm. c

on

du

cta

nce

(a.

u.)

1

1.1

0.9

FIGURE 2. Contour plot for the conductance for all fields studied. light (dark) color represents low (high) bias. Note that the low bias region changes con-tinuously with increasing fields, while the high bias region is highly discontinuous at 6 Tesla.

In summary, we have shown that the tunneling den-sity of states is highly modified by the presence of high magnetic fields – high currents. The gap-like fea-ture, at high bias, shifts discontinuously, while the low bias region evolves continuously. We conclude that the gap-like feature bias depends strongly on cur-rents, but the shift is anisotropic and due to a combina-tion of both strong currents and high magnetic fields.

ACKNOWLEDGMENT

This work was supported by the Heinrich Hertz Minerva center for High Temperature super-conductivity, the Israel Science Foundation, the Oren Family Chair of Experimental Solid state physics.

REFERENCES

1. C.R. Hu , Phys.Rev. Lett. 72, 1526 (1994). 2. M. Fogelström et al., Phys.Rev. Lett. 79, 281 (1997). 3. R. Beck et.al., Phys.Rev.B 69, 144506 (2004). 4. R. Beck et.al., Phys.Rev.B 72, 104505 (2005). 5. Y. Radzyner, A. Sheulov and Y. Yeshurun, Phys.Rev. B

65, 100513(R) (2002).

Chapter 8

Supplementary results

Previous tunneling measurements into YBa2Cu3O7−x found that, in some cases, the

Zero-Bias Conductance Peak (ZBCP) spontaneously splits without applying any mag-

netic fields. In addition, Dagan et al. [13, 34] showed that spontaneous splitting occurs

only in overdoped films and that its value increases with doping. The magnetic field-

induced splitting was also found to be doping-dependant where the splitting rate

decreases as the doping level moves away from optimum.

In the following, we show additional experimental results, from tens of junctions

with different doping levels and in high magnetic fields. These experimental results

give new evidence for a modification in the order-parameter symmetry in the vicinity

of optimum doping.

67

68 Supplementary results

8.1 Non-concomitance in spontaneous and induced

ZBCP splitting

Two opposite views have been expressed regarding the occurrence of spontaneous

symmetry breaking in cuprates at low temperatures. Greene et al. [42] claimed that

spontaneous and field splitting occur concomitantly at a given junction and that it

is only because the width of the tunneling cone varies from junction to junction that

the ZBCP splitting is prevented or observed.

The argument presented by Greene et al. is that splitting is a result of a Doppler

shift of the bound states energy as presented in Sec. 2.5.1. The Doppler shift is equal

to vS · pF , where vS is the superfluid velocity of surface currents, and pF is the Fermi

momentum of tunneling particles. When the tunneling cone is very narrow, the scalar

product becomes too small to give a measurable splitting.

By contrast, Dagan and Deutscher[13] reported that spontaneous splitting is

present only in overdoped samples, while field splitting is present both in under-

doped and overdoped samples, albeit with a rate that becomes smaller as one moves

away from optimum doping on both sides (i.e. underdoped and overdoped). It is

important to point out, that Dagan’s work was in the vicinity of optimum doping

with changes in doping levels that caused no more than a 10% reduction in the film’s

Tc.

In the case that the ZBCP splitting is primarily due to an imaginary idxy or is

8.1. Non-concomitance in spontaneous and induced ZBCP splitting 69

order-parameter component, either spontaneous or field-induced, which removes the

order-parameter nodes, it will appear for the (110) surface orientation as a finite

excitation energy, irrespective of the width of the tunneling cone. In such a case, the

tunneling particles penetrate into the superconductor with a momentum that has the

orientation of the (removed) node.

Most previous works on this subject used tunneling measurements performed at

4.2K. In our case, we used an indium counter electrode and, at 4.2K, the indium is

above its superconducting critical temperature. At this temperature, thermal smear-

ing can not be ruled out as the cause for the absence of spontaneous ZBCP splitting.

In order to check the possibility that a small, but finite splitting is not observed in

our optimally doped samples due to thermal smearing, we performed measurements

at temperatures down to 0.3K. The problem is then, of course, that the indium

counter electrode is also superconducting, and hence the indium gap dominates the

tunneling characteristic at low bias. For example, see Fig. 8.1 taken at 0.3K for a

YBa2Cu3O7−x /In junction at zero magnetic field.

Quenching superconductivity in the indium counter electrode by applying a small

magnetic field is easy since indium’s critical field is relatively small (∼ 0.03T). How-

ever, such a magnetic field by itself can induce field splitting, when applied perpen-

dicular to the CuO2 planes. As shown by Krupke et al. [15], a field applied parallel

to the CuO2 planes does not produce ZBCP splitting. We used this property of our


-2 0 20.0

0.5

1.0

1.5

2.0

norm

.co

nduc

tanc

e (a

.u)

Bias (mV)

1.3mV

Figure 8.1: Normalized tunneling conductance of 4 different YBa2Cu3O7−x /In junc-tions on two different samples taken at 0.3K and zero magnetic field. The indiumgap dominates the zero bias region, masking the zero-bias conductance peak shownat higher temperatures/magnetic fields when the indium is non-superconducting.

films to surmount the above experimental difficulty.

Combining measurements at low temperatures, and at both field orientations -

perpendicular to the CuO2 planes that induce splitting and parallel to the CuO2

planes that do not induce additional splitting - should resolve the question of the

concomitant nature of spontaneous and field-induced splitting. We note that, in both

configurations, the magnetic field is parallel to the film’s surface.

The result of such an experiment is shown in Fig. 8.2. The sample is slightly

underdoped with a critical temperature of 89K. The black solid line shows a sharp

ZBCP without any observable splitting. This measurement was done when a relative

low magnetic field is applied parallel to the CuO2 planes (i.e. perpendicular to the

8.1. Non-concomitance in spontaneous and induced ZBCP splitting 71

-20.0 -10.0 0.0 10.0 20.0

0.9

1.0

1.1

1.2

T=0.3K

dI/d

V (a

rb. u

nt.)

Bias (mV)

H="0" (0.1 T, H c) H=1T (H||C)

Figure 8.2: Tunneling conductance for a (110) film taken at 0.3K. The black linemeasured in magnetic field of 0.1 T applied parallel to the CuO2 planes where theindium counter electrode is normal without inducing ZBCP splitting. The red curve isfor 1 T applied perpendicular to the CuO2 planes, where induced splitting is observed.

c-axis and parallel to the surface) in order to quench superconductivity in the indium

counter electrode without inducing ZBCP splitting. Therefore, the black line repre-

sent an effective “zero field” measurement at 0.3K. An upper limit for the spontaneous

splitting, for this junction, is set to be smaller than 2KbT = 0.06meV . We note that

even at 16 T, we do not observe any ZBCP splitting under this configuration, which

ensures the sample’s orientation.

Nevertheless, the situation is very different when the magnetic field is applied

perpendicular to the CuO2 planes (i.e. parallel to the c-axis and to film surface), as

presented in the red curve in Fig. 8.2. Here, for an external magnetic field of 1 T,

the ZBCP splits up to a value of 2.2 meV.


Therefore, in the slightly underdoped samples, we find that spontaneous and mag-

netic field-induced ZBCP splitting can occur independently at a given junction. It is

best seen in optimally doped samples having the (110) orientation.

8.2 On the origin of spontaneous splitting

Next, we review the origin for the spontaneous ZBCP splitting. As in the magnetic

case, any currents can produce a Doppler shift [23]. In zero magnetic field, sponta-

neous currents can produce ZBCP splitting. For example, a circulating super-current

resulting from a trapped flux near the surface can produce a Doppler-shift that will

be observed as a ZBCP splitting in a tunneling spectrum[27].

Another option could be a secondary imaginary component to the superconducting

order-parameter. This option was discussed in terms of a quantum critical point in

the vicinity of optimum doping. [13, 43] In such a case, when the order-parameter has

an additional ±is or ±idxy component, it will spontaneously produce surface currents

due to the phase gradient, resulting in a split ZBCP in the tunneling density of states.

Both cases break time reversal symmetry, as the spontaneous currents flow in a

specific direction. In such a case of time reversal symmetry breaking, applying addi-

tional currents should result in either increasing or decreasing the total current. We

stress that, in terms of energy, both plus and minus sign components are degenerate.

We impose a strong surface current by applying a magnetic field parallel to the

8.2. On the origin of spontaneous splitting 73

Figure 8.3: Theoretical calculation by Fogelsrom et al. for the ZBCP splitting, δ(H),as a function of the magnetic field and strength of the subdominant pairing channel.Subdominant channels: (a), (b) A1g, (c), (d) B2g. Note the asymmetry at differentmagnetic field polarities when a subdominant channel appears. Adopted from [44]

surface and perpendicular to the CuO2 planes. Therefore, we may be able to check

whether time reversal symmetry breaking occurs spontaneously in the system by

measuring the difference in ZBCP splitting observed for magnetic fields of opposite

polarity.

As mentioned by Fogelstrom et al. [44], in the case of spontaneous broken time

symmetry, a strong asymmetry in the ZBCP splitting should be observed for different

polarities (see Fig. 8.3).

However, we find no differences in the tunneling spectra, within our experimental

resolution, at both polarities. This is shown in Fig. 8.4. An experiment, similar

in concept, was conducted by Tsuei et al. where they measured the spontaneous

half flux-quantum vortex in a tri-crystal experiment and found no difference between


-10 0 10

0.18

-6 -4 -2 0 2 4 60.15

0.16

dI/d

V (

-1)

bias (mV)

+1T -1T

Figure 8.4: Tunneling conductance taken in opposite magnetic field polarities at 4.2K.Within the measurement resolution we find no change between the two spectra in bothpolarities. Insert: full measured bias region where no changes are noticed as well.

vortices at opposite polarities.[45]

Furthermore, if time reversal symmetry is spontaneously broken, we expect that,

when we increase the magnetic field for a virgin sample, we shall find that the sponta-

neous ZBCP split value reduces with increasing magnetic fields about half the time.

This would be the case if the induced current is opposite to the spontaneous one.

However, in over 100 junctions measured in this research, not even once did we ob-

serve that the spontaneous ZBCP splitting decreased with increasing magnetic fields.

Measurement of the ZBCP splitting in a complete hysteresis loop with both polarities

is shown in Fig. 8.5.

We showed in Sec. 2.5.1 that the Doppler shift could be the result of surface

8.2. On the origin of spontaneous splitting 75

0 1 2 3 4 5 61.5

2.0

2.5

3.0

3.5

0 6 T6 0 T0 -6 T-3 0 T

(mV

)

0H|(Tesla)

Figure 8.5: Zero-bias conductance peak splitting, δ, as a function of the absolutemagnetic field in both polarities. We found no evidence that the polarity of themagnetic filed influences the peak position for a given field.

Meissner currents [23] or nearby circulating vortex currents [27]. In both cases, the

Doppler shift will result in ZBCP splitting. However, the effect of each should be

opposite as they originate from opposite currents. Therefore, as one increases the

magnetic field and the nearby vortex approaches the surface, it is expected that the

ZBCP splitting should reduce at high fields. This was not observed in any of our

samples, up to fields of 32.4T.

As previously shown, the Doppler shift effect, due to surface Meissner currents, is

negligible in decreasing fields (see chapters 4 and 5). However, the effect of a nearby

vortex [27] could still take place in a decreasing magnetic field. In order to check this

possibility, we note that when decreasing the magnetic field from the maximum value


reached, the vortex current will have to overcome opposite Meissner currents present

in increasing magnetic fields. Since the Doppler effect (and hence the ZBCP splitting)

is only proportional to the current magnitude, at some decreasing magnetic field the

net current (Meissner and nearby vortex) should be zero. In this case, a ZBCP should

appear at a finite magnetic field. As shown in Fig. 8.5 the ZBCP splitting is always

higher, at any magnetic field, than the zero-field splitting. This rules out that the

splitting in a decreasing field is due to the effect of a nearby vortex.

Since our measurements, as well as the tri-crystal, are macroscopic in size, domains

with alternating spontaneous current directions could not be ruled out. In such a

case, in the domain wall region, there should be a zero net current and, therefore,

no spontaneous current. Since the order-parameter changes over a length scale set

by the coherence length, one should find nanometer scale regions (the domain wall

region) where the splitting of the ZBCP is zero, while, in other regions (inside the

domains), the splitting should be finite. Since both techniques probe on macroscopic

length scales, only microscopic measurements, for example with a scanning tunneling

microscope, may be able to probe such domain walls.

Furthermore, in the domain wall region, the order-parameter symmetry should be

purely d -wave . Therefore, measurements aiming at detecting node-line excitations,

such as thermal conductivity, might mistakenly pick up only those in the domain wall

region.

8.3. The effect of doping 77

8.3 The effect of doping

Previous works by Dagan et al. found that changing the doping levels (in the vicinity

of optimum doping), modifies the tunneling spectrum at both zero magnetic field

and with applied magnetic fields.[13, 34] This effect was interpreted as evidence for a

quantum phase transition in the superconductor order-parameter at optimum doping.

We showed in Ch. 5 that in decreasing fields, for nearly optimally doped samples,

the ZBCP splits as a square root of the magnetic field. This behavior was found

to be robust for high magnetic fields (up to 16 T) and various film thicknesses. We

concluded that it can be explained by an induced order-parameter node-removal at

high magnetic fields. [18, 29–31]

Here we continue our tunneling study at high magnetic fields for films at various

doping levels. Representative ZBCP splitting values in decreasing magnetic fields for

different junctions are shown in Fig. 8.6. We note a funnel shape behavior indicating,

that in high magnetic fields, the ZBCP splitting follows the rule of a square root

behavior in all cases.

Theoretical studies by Asano et al. [46–48] and Kalenkov et al. [49] show that

surface impurities could result in a spontaneous ZBCP splitting. These models predict

that scattering of impurities will cause bound states that will dominate the low bias

spectrum. However the Andreev - Saint-James bound states will most probably still

be present, and a three peaked structure at the zero-bias should be present. We did


0.1 1 10

1

(mV

)

0H(Tesla)

1.1H1/2

Figure 8.6: Zero-bias conductance peak splitting, δ, versus decreasing magnetic fieldspresented on a log-log scale. Each symbol indicates different film. In high magneticfields, all the data follow a square root behavior.


not observe such behavior in any of the junctions presented here.

Moreover, according to these models, the “impurity spontaneous splitting” should

be proportional to the amount of impurities. In the case of a clean junction, a ZBCP

should be present. However, when a magnetic field is present, a splitting via an

Aharonov-Bohm-like phase shift will occur.[46] The splitting will be more pronounced

as more impurities will be present at the junction’s interface. In the case of a clean

interface, no magnetic field splitting should be observed and vice-versa.

The data in Fig. 8.6 shows the opposite, as any junction with a spontaneous

splitting, splits less at a given low field, than a non-spontaneously split one. This

rules out impurities as a possible explanation for spontaneous splitting.

We found a scaling law to fit our overdoped data in decreasing fields where the

ZBCP splitting, δ(H), follows the equation:

δ(H)2 = δ20 + A2 · H (8.3.1)

here, δ0 is the spontaneous ZBCP splitting, and A is a coefficient in the order of

1.1 meV/T1/2. This is in agrement with our result at optimum doping shown in

chapter 5 where no spontaneous splitting was measured and the splitting followed the

same rule. In addition, at H ≫ δ20/A

2 we expect to see, for all doping levels, a square

root behavior, as indeed observed (see Fig. 8.6).

We interpret the square-root behavior at nearly optimum doping as an indication

of an order-parameter node-removal. However, all theories treated the node-removal


Figure 8.7: Tunneling con-ductance in a decreasing(black line) field-cooled(red line) and increasingmagnetic fields at 0.3K.Panel (a) at 3T and (b) at10T.

0.35

0.40

0.45

(a)

Decreasing field Field cooled Increasing field

3T

dI/d

V(

-1)

-20 -10 0 10 20

0.35

0.40

0.45

(b)

dI/d

V (

-1)

10T

Bias (mV)

mechanism in the case of a pure d -wave order-parameter symmetry.[29–31] Assum-

ing that the spontaneous splitting is an indication of a change in order-parameter

symmetry to dx2−y2 ± idxy or dx2−y2 ± is [13, 23, 34], it mainly affects the node lines.

Therefore, if the order-parameter symmetry is modified in overdoped samples, it

will affect the node line excitation spectrum. At high enough fields, the perturbation

creating the spontaneous splitting, no longer dominates the spectrum since it is mainly

affected by the high cyclotron-frequency. Therefore, Eq. 8.3.1 represents the effect


of both the node-line excitation and the spontaneous change in the order-parameter

from the d -wave symmetry.

As pointed out by Gor’kov and Schrieffer the node-line excitations, will be affected

by currents, as the levels should be Doppler-shifted and smeared.[30] However, we

note that our tunneling data are only sensitive to the first level (n = 1 in Eq. 2.5.9).

This level should appear in all field configurations such as increasing, decreasing

and field cooled conditions as it is magnetic field dependent. However, an additional

contribution, via the Doppler-shift mechanism, is expected when the screening current

is at a maximum (see Sec. 2.5.1), i.e. in increasing magnetic fields.

We compare the tunneling spectrum in all three magnetic field configurations in

Fig. 8.7. We note that while the ZBCP splitting is different for each configuration,

the zero bias region up to a few meV is only shifted by a constant value. This is

shown in Fig 8.8.

In addition, we notice that the zero-bias region transforms from an inverted cusp

feature at low bias to a U-shape in high magnetic fields. To illustrate this, we show,

in Fig 8.9, the derivative of the conductance curve (i.e.


-15 -10 -5 0 5 10 15

0.35

0.40

dI/d

V(s

)

Bias (mV)

Decreasing Field cooled Increasing

8 T

Figure 8.8: Low bias tunneling conductance in decreasing (black line) field cooled (redline) and increasing magnetic fields at 0.3K and in 8T. The conductance is shifted bya constant to match the zero bias conductance.

-10 -5 0 5 10

-20

0

20 3T 15T

d2 I/dV

2 (-2

)

Bias (mV)

Figure 8.9: d2I/dV 2 vs. V for the junction shown in Fig. 8.7 in increasing magneticfields at 0.3K.

Chapter 9

Summary and conclusions

We measured the tunneling conductance of YBa2Cu3O7−x thin films in high magnetic

fields. Using the tunneling spectra, we studied the superconductor’s density of states,

induced currents and the order-parameter symmetry.

This work aimed at answering the question of whether the Zero-Bias Conduc-

tance Peak (ZBCP) splitting in magnetic fields occurs solely due to the Doppler-shift

of surface-bound states [23] or whether it also probes field induced finite energy levels

along the d -wave node-line[29–31]. We conclude, from various experimental observa-

tions, that it is impossible to explain our data in the framework of a Doppler-shift

alone. In addition, there are supporting evidence for energy levels which remove the

d -wave nodes in magnetic fields. We showed under which conditions these levels can

be measured, and corresponded these levels to theoretical predictions [29–31] up to

very high fields [17, 18, 20]. Below, we summarize our experimental findings and its

83

84 Summary and conclusions

correlation to our conclusions.

In our geometry, the field is applied parallel to the film surface. In this case, Meiss-

ner surface currents are governed by surface barriers [24–26]. Therefore, in increasing

fields, when vortex entry is prevented by the barrier, the Meissner surface currents

increase, and the Doppler-shift should be pronounced. Nevertheless, in decreasing

fields, there is no barrier for flux exit, and the Meissner surface currents are minimal.

This explains the observed ZBCP splitting hysteresis and enables us to separate the

Doppler shift contribution from any other contributions to the ZBCP splitting.[18]

This is done by measuring the difference between increasing and decreasing ZBCP

splitting which fits the Doppler-shift effect predication.[17, 18, 44]

Large ZBCP splitting in [110] oriented films in decreasing fields was measured.

Moreover, the splitting in decreasing fields was found to be robust up to high fields and

to be thickness independent.[17] These facts cannot be explained in the frame work

of the Doppler shift effect as the Meissner currents are negligible in decreasing fields

and depend on many of the junctions’ parameters, such as the tunneling cone, films

thickness and quality. Therefore, we find the splitting in decreasing fields to indicate

a node-removal mechanism that creates finite node-line energy levels. [17, 29–31]

Such levels scale as a square-root of the applied magnetic field, as experimentally

observed.[17, 20]

In addition, the ZBCP splitting in magnetic fields was higher when tunneling

85

into [110] then into [100] oriented films. We explain this by taking into account

that planar tunneling mainly probes excitations that occupy energy levels inside the

tunneling cone. Therefore, our experimental observation supports evidence that the

splitting seen in decreasing fields is mainly due to nodal energy levels that remove

the d -wave node.[17, 18]

Another theoretical approach to explain the ZBCP splitting was given by the effect

of a nearby vortex approaching the surface.[27] In such a case, the vortex-circulating

currents will Doppler shift the surface bound states. However, since the vortex cur-

rents flow in opposite direction to the Meissner surface screening currents, it will

produce non-monotonic ZBCP splitting values at high increasing magnetic fields and

when decreasing the field from the maximum field reached. In our measurements (up

to 32.4T), none of these behaviors occured, and the ZBCP splitting always increased

(decreased) in increasing (decreasing) magnetic fields. This experimental evidence

rules out the effect of a nearby vortex as an explanation for ZBCP splitting.

In addition, we showed that spontaneous splitting and magnetic field splitting

can occur non-concomitantly. This is in contrast to a previous publication[42] and

additional support to our claim that ZBCP splitting, in [110] oriented films, is mainly

due to nodal energy levels which are not affected by the tunneling cone.

We studied the splitting evolution in overdoped films. In these films, the ZBCP

split spontaneously at zero magnetic field. Although the ZBCP splitting rate in low

86 Summary and conclusions

magnetic fields is smaller than in optimally doped films, in high magnetic fields,

the ZBCP splitting rate recovers and becomes essentially doping-independent. The

observed behavior indicates that perturbation in the order-parameter symmetry, in

particular at the d -wave node, occurs around optimum doping. This is an additional

indication for a quantum critical point in the vicinity of optimum doping. [43]

The nature of the spontaneous splitting was discussed in terms of a spontaneously

induced additional component, having either ±is or ±idxy symmetry, to the ground

state order-parameter. Such an additional order-parameter symmetry will break time-

reversal symmetry and involves surface currents. Therefore, we can expect that the

ZBCP splitting will be asymmetric between different field polarities.[44] However, we

found no experimental difference between the tunneling spectra of opposite magnetic

field polarities. This suggests the existence of domains, having alternating plus and

minus additional order-parameter symmetries, in the system as they are energetically

degenerated. Moreover, at the domain wall boundary, the order-parameter is purely

d -wave . This can explain why other methods aiming at nodal excitation, might

probed the domain walls region and mistakenly ruled out the perturbation for the

d -wave symmetry we found.

Furthermore, the calculations for the nodal energy levels [30, 31] was made under

the assumption that the field is homogeneous. As mentioned by Janko, [32] vortices

and their accompanying circulating currents smear the levels, making them hard to

87

detect. Our experimental configuration is actually prefect to overcome this problem,

as we measure at the surface of thin films with the magnetic field applied parallel to

surface.

Finally, we studied the gap-like feature on the superconductor gap energy scale.[19,

41] We found, in optimally doped samples, having the [110] orientation, a transition

in the gap-like feature position and amplitude in high magnetic fields. We proposed

that this transition is due to the induced super-currents and not directly due to the

field. This possibly indicates a fully gapped order-parameter at high nodal currents.

However, a transition between different vortex states, having different gap values and

sensitivities to the nodal currents cannot be ruled out.

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, המוליכות במתח אפס-שונים האחראים לפיצול של שיאהנדון במנגנונים .בשדה מגנטי גבוה

.מנגנון הסרת הצומת בפרמטר הסדרנובע בעיקרו מ יורד פיצול בשדה מגנטיונראה כי ה

נראה כי . המוליכות במתח אפס בשדה מגנטי-נדון בתופעת החשל בפיצול שיא, כמו כן

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.ם פני שטחקטן בצורה משמעותית בשל העדר מחסו

העל -מתחים המאפיינים את פער האנרגיה של מוליךאופייני המנהור בנראה כי , בנוסף

נדון בתופעה במונחים של מעבר פאזה . י רציפה בשדות מגנטים חזקיםתמשתנים בצורה בל

יתכן ונובעת מהזרמים המושרים ,תופעה זו. מסדר ראשון למצב בו פער האנרגיה מלא יותר

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נראה כי . על אופייני המנהור בשדות מגנטים חזקיםחמצן נדון בהשפעת אילוח , לבסוף

יחס בו הפיצול שווה , יהמוליכות במתח אפס מציית לחוק אוניברסאל-שיא, בשדות חזקים

, ורות להתנהגות האוניברסאליתנדון במספר מק. לשורש הריבוע של השדה המגנטי החיצוני

לשינוי בסימטריה של פרמטר השדה היכר גות בשדה נמוך הינה סימן ר כי ההתנהונשע

. יאופטימאלבקרבת אילוח

תקציר

י "ע. ים חזקיםי בנוכחות שדות מגנטYBa2Cu3O7-xהעל -מדדנו את מוליכות המנהור במוליך

חקרנו את צפיפות המצבים והסימטריה של פרמטר הסדר ,שימוש בצמתי אינדיום מישוריים

.העל-של מוליך

מוליכות במתח אפס - על ידי שיאבמישוריי תחמוצת הנחושת מאופייניםמוליכות המנהור

המאפיין הראשון הינו סימן ההיכר של .העל-ושיא מוליכות במתח פער האנרגיה של מוליך

. של פער האנרגיהיבעוד השני מצביע על ערכו המקסימאל, dסימטרית בעל פרמטר הסדר

. בחנו את התפתחות שני מאפיינים אלו בנוכחות שדה מגנטי חזק,בעבודה זו

יאים בנוכחות שדה מגנטי המאונך למישורי אפס מתפצל לשני שהמוליכות במתח -שיא

שיא , כי כאשר שומרים על השדה המגנטי מקביל לפני השטח, נראה. תחמוצת הנחושת

כי בשכבות אנמצ. המוליכות מתפצל בצורה שונה עבור שכבות עם סידור גבישי שונה

ח אפס המוליכות במת-פיצול שיא, מאונך לפני השטח] 110[בעלות סידור גבישי עם כיוון

על -מנהור לשכבות דקות מוליכות בנוכחות בטמפרטורה גבוהה

חזקיםשדות מגנטיים מאת ברקאי-רועי בק

"דוקטור לפילוסופיה"חיבור לשם קבלת התואר

בית הספר לפיסיקה ואסטרונומיה, אביב-אוניברסיטת תל ישראל, אביב-תל

ו"אדר תשס

Documents

TEL AVIV UNIVERSITY - UCSB MRSEC › ~roy › ThesisBeck.pdfﬁelds” by Roy Beck-Barkai in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy. Dated: