Superconductor-Insulator Transition Induced by

Electrostatic Charging in High Temperature

Superconductors

A DISSERTATION

SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL

OF THE UNIVERSITY OF MINNESOTA

BY

Xiang Leng

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

Doctor of Philosophy

Allen M. Goldman, Adviser

November, 2011

c© Xiang Leng 2011

ALL RIGHTS RESERVED

Acknowledgements

I want to thank a lot of people for helping and supporting me in completing

my Ph.D research.

I would like to express my sincere gratitude to my advisor Prof. Allen M.

Goldman for the continuous support of my Ph.D study and research, for his pa-

tience, motivation, enthusiasm, and immense knowledge. His guidance helped me

in all the time of research and writing of this thesis.

I would like to thank the rest of my thesis committee: Prof. Boris Shklovskii,

Prof. C. Daniel Frisbie and Prof. Martin Greven, for their encouragement, in-

sightful comments and good questions.

My sincere thanks also goes to Dr. Yu Chen, Dr. Javier Garcia-Barriocanal,

Dr. Yen-Hsiang Lin, Dr. Chun Yu Wong, Dr. Alexy Kobrinskii, Shameek Bose

and Mingjing Ha, for their help with the experiments.

I thank my fellow labmates in my group: Stephen Snyder, Yeonbae Lee, Ilana

Percher, JJ Nelson, Joe Kinney, Boyi Yang, Olesya Koroteeva and Terry Bretz-

Sullivan for their help and for all the fun we have had in the last four years.

I would like to thank my family: my parents, Qicheng Leng and Juhong Feng,

for their support and encouragement to complete this work; my wife Ruihong

Zhang and my daughter Sarah Leng for giving me so much happiness in the last

several years.

i

I would like to acknowledge that this work was partially funded by the National

Science Foundation under grant NSF/DMR-0709584 and 0854752.

ii

Abstract

Ultrathin YBa2Cu3O7−x films were grown on SrTiO3 substrates in a high pres-

sure oxygen sputtering system to study the superconductor-insulator transition by

electrostatic charging. While backside gating using SrTiO3 as a dielectric induces

only small TC shifts, a clear transition between superconducting and insulating be-

havior was realized in a 7 unit cell thick film using an ionic liquid as the dielectric.

Employing a finite size scaling analysis, curves of resistance versus temperature,

R (T ), over the temperature range from 6 K to 22 K were found to collapse onto

a single function, which suggests the presence of a quantum critical point. How-

ever the scaling failed at the lowest temperatures indicating the possible presence

of an additional phase between the superconducting and insulating regimes. In

the presence of magnetic field, a cleaner superconductor-insulator transition was

realized by electrostatic charging. A scaling analysis showed that this was a quan-

tum phase transition. The magnetic field did not change the universality class.

Further depletion of holes caused electrons to be accumulated in the film and the

superconductivity to be recovered. This could be an n-type superconductor. The

carriers were found to be highly localized.

By changing the polarity of the gate voltage, an underdoped 7 unit cell thick

film was tuned into the overdoped regime. This process proved to be reversible.

Transport measurements showed a series of anomalous features compared to chem-

ically doped bulk samples and an unexpected two-step mechanism for electrostatic

doping was revealed. These anomalous behaviors suggest that there is an elec-

tronic phase transition in the Fermi surface around the optimal doping level.

iii

Contents

Acknowledgements i

Abstract iii

List of Tables vi

List of Figures vii

1 Introduction 1

1.1 Crystallographic structure . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Electronic structure . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Quantum phase transition . . . . . . . . . . . . . . . . . . . . . . 9

1.5 Motivation and outline . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Sample preparation and characterization 14

2.1 Substrate treatment . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Film deposition using a high pressure oxygen sputtering system . 15

2.3 Film characterization . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Field effect device development 25

iv

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Properties of SrTiO3 . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Backside gating using SrTiO3 as a dielectric material . . . . . . . 27

3.4 Properties of the ionic liquid . . . . . . . . . . . . . . . . . . . . . 29

3.5 Top gating using an ionic liquid as a dielectric material . . . . . . 31

4 Experimental results and discussion 34

4.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1.1 Backside gating using SrTiO3 as a dielectric . . . . . . . . 35

4.1.2 Top gating using an ionic liquid as a dielectric . . . . . . . 35

4.2 Results of backside gating using SrTiO3 as a dielectric . . . . . . 36

4.3 Results of top gating using an ionic liquid as a dielectric . . . . . 40

4.3.1 Samples of different thicknesses . . . . . . . . . . . . . . . 40

4.3.2 The evolution from superconductor to insulator in a 7 UC

thick sample . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3.3 Quantum phase transition . . . . . . . . . . . . . . . . . . 51

4.3.4 Quantum critical behavior in the presence of magnetic field 53

4.3.5 Superconductivity on the electron-doped side . . . . . . . 59

4.3.6 Anomalous behavior on the overdoped side . . . . . . . . . 59

5 Conclusions and Future Directions 72

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

References 76

Appendix A. Acronyms 90

v

List of Tables

A.1 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

vi

List of Figures

1.1 Crystal structure of YBa2Cu3O7−x . . . . . . . . . . . . . . . . . 3

1.2 Classification of bulk high-Tc cuprates . . . . . . . . . . . . . . . 4

1.3 Energy levels for a Mott insulator . . . . . . . . . . . . . . . . . . 6

1.4 Crystal-field splitting of 3d orbitals. . . . . . . . . . . . . . . . . . 7

1.5 Generic phase diagram of the cuprates . . . . . . . . . . . . . . . 10

2.1 AFM images of STO substrates . . . . . . . . . . . . . . . . . . . 16

2.2 X-ray diffraction patterns of YBCO films of different thicknesses. 19

2.3 Rocking curve of the (005) peak of a 5.5 nm thick YBCO film. . 20

2.4 Rocking curve of the (005) peak of an 8 nm thick YBCO film. . . 21

2.5 X-ray reflectivity data of films of different thicknesses. . . . . . . . 22

2.6 Comparison of X-ray reflectivity raw data with fitted curves. . . . 23

2.7 Typical R(T) curve of a 15 UC thick YBCO film. . . . . . . . . . 24

3.1 Sketch of a backside gated FET device . . . . . . . . . . . . . . . 28

3.2 Cartoon of an FET device using an ionic liquid . . . . . . . . . . 30

3.3 Capacitance-voltage curve of an ionic liquid . . . . . . . . . . . . 32

3.4 Cartoon of the FET structure used to gate YBCO films . . . . . . 33

4.1 R(T) of two backside gated YBCO films . . . . . . . . . . . . . . 37

4.2 R(T) of a backside gated 3 UC thick YBCO film . . . . . . . . . . 38

4.3 R(T) of a top gated 6 UC thick YBCO film. . . . . . . . . . . . . 44

vii

4.4 R(T) of a top gated 8 UC thick film. . . . . . . . . . . . . . . . . 45

4.5 R(T) of a top gated 10 UC thick film. . . . . . . . . . . . . . . . . 46

4.6 R(T) of a top gated 7 UC thick YBCO film. . . . . . . . . . . . . 47

4.7 Carrier concentration calculated from the normal resistance. . . . 49

4.8 Phase diagram of a 7 UC thick YBCO film . . . . . . . . . . . . . 50

4.9 Finite size scaling analysis of a 7 UC thick YBCO film . . . . . . 52

4.10 R(T) curves in the presence of magnetic field . . . . . . . . . . . . 57

4.11 Finite size scaling analysis in the presence of magnetic field . . . . 58

4.12 R(T) curves on the electron doped side . . . . . . . . . . . . . . . 60

4.13 V-I curves at VG =1.7 V . . . . . . . . . . . . . . . . . . . . . . . 61

4.14 V-I curves at VG =2.0 V . . . . . . . . . . . . . . . . . . . . . . . 62

4.15 R(T) at different gate voltages. . . . . . . . . . . . . . . . . . . . 65

4.16 TC and normal resistance vs. doping . . . . . . . . . . . . . . . . 67

4.17 Hall resistance at different gate voltages . . . . . . . . . . . . . . 69

viii

Chapter 1

Introduction

High-TC superconductors (HTSCs), such as the cuprates, have been intensively

studied for more than two decades. However many basic questions still remain

open and thus far there is no widely accepted theory to describe their properties.

One of the most important questions is the nature of superconductor-insulator (SI)

transition at zero temperature induced by varying parameters such as thickness,

magnetic field or carrier concentration. This SI transition is believed to be a

quantum phase transition (QPT) and studying this transition will promote further

understanding of the fundamental physics of HTSCs.

1.1 Crystallographic structure

There are several families of cuprates (categorized by the elements they contain)

but they have a common perovskite structure. A typical structure of YBa2Cu3O7−x

(YBCO) is shown in Figure 1.1. In the middle of the unit cell there are two copper-

oxide (CuO2) planes forming two CuO5 pyramids with apical oxygens. If there

were only one CuO2 plane then one would expect a CuO6 octahedron, as in the

1

2

case of La2−xSrxCuO4 (LSCO). It is widely accepted that the superconducting

properties are determined by carriers moving within the weakly coupled CuO2

planes, while the other layers serve as reservoirs to dope electrons or holes onto

the CuO2 planes. Based on the number of CuO2 planes in one unit cell (UC),

the cuprates can be classified into single-layer materials, bilayer materials, trilayer

materials, and so on. The first 3 classes are illustrated in Figure 1.2 [1]. On the

other hand, one can also categorize cuprates based on the location of chemical dis-

order. In Figure 1.2, patterns (a), (b) and (c) represent three different locations of

chemical disorder in cuprates, where pattern (a) corresponding to disorder located

near the apical oxygen (also called A-site disorder), pattern (b) corresponding to

disorder located in between CuO2 planes (thus there is no such disorder in single-

layered cuprate) and pattern (c) corresponding to oxygen defects in the CuOx

chains in YBCO or at similar positions in other families. In general, disorder of

pattern (c) is expected to have the weakest effect since it is far away from the

CuO2 planes. On the other hand, disorder of pattern (a) is expected to be the

strongest since this kind of disorder will change both the lattice and the electronic

properties of the apical oxygen, which has a serious effect on the CuO2 planes. As

for (b) type disorder, the space between CuO2 planes will serve as a buffer and

reduce its effect.

1.2 Electronic structure

In cuprates, the Copper ion (Cu2+) has a 3d9 configuration. 3d electrons have

tenfold degeneracy (including spins), which can be lifted by the anisotropic crystal

field as shown in Figure 1.4 [2]. Due to the Perovskite structure the Copper

ion faces a tetragonal environment which leads to a half filled dx2−y2 orbital.

3

Figure 1.1: Crystal structure of YBa2Cu3O7−x

4

Figure 1.2: Classification of bulk high-Tc cuprates in terms of the site of disorderand the number of CuO2 planes. Materials belonging to the same family are in-dicated by the same color. The Halogen family denotes (Ca, Sr)2CuO2A2 (A=Cl,F) based materials. The Bi family denotes Bi22(n-1)n(n=1,2,3). The Pb familydenotes Pb2Sr2Can−1Cun+1Oz. The 1L Tl family denotes single-Tl-layer cuprates,TlBa2Can−1CunO3+2n+δ. The 2L Tl family denotes two-Tl-layer cuprates,Tl2Ba2Can−1CunO4+2n+δ. The La family denotes La2Can−1CunO2+2n. The YBCOfamily denotes YBa2Cu3O6+δ. The Hg family denotes HgBa2Can−1CunO2+2n+δ

(From Ref. [1].)

5

Traditional band theory predicts this configuration to be a conductor, while we

now know the parent compound of cuprates is a so-called Mott-insulator. This is

different from a conventional band insulator, in which the Fermi level lies in the

band gap and the band underneath is completely filled. A Mott-insulator has a

partially filled “conduction” band but the strong electron-electron interactions

prevent the carriers from moving around. In other words, the strong electron-

electron interactions split the partially filled band into two sub-bands at the Fermi

level as illustrated in Figure 1.3 [2]. If the energy level of a p orbital (εp) is much

lower than that of a d orbital (εd), i.e., |εd − εp| > U , where U is the electron-

electron interactions, the band gap is mainly determined by U. This is called a

Mott-Hubbard insulator(Figure 1.3(a)). On the other hand, if |εd − εp| < U , the

band gap will be determined by the hybridization of a 3d orbital and a ligand p

orbital. This is called a Charge-Transfer insulator as shown in Figure 1.3(b). In

cuprates the 3d orbitals of Copper are close to the 2p orbitals of Oxygen. Thus

the parent compound of a cuprate is a Charge-Transfer-Insulator. In summary, it

is the interaction between the Cu 3dx2−y2 orbital and the O 2px and 2py orbitals

that splits the half filled d-band into two sub-bands, leaving an insulating gap in

the parent compounds. A small amount (5%) of carriers doped into this Mott-

insulator will cause an Insulator-Metal transition at high temperature and an

Insulator-Superconductor transition at low temperature.

1.3 Phase diagram

Now we know cuprates can be viewed as doped Mott insulators. A temperature-

doping phase diagram for hole-doped cuprates is shown in Figure 1.5. The number

6

Figure 1.3: Energy levels for a Mott insulator (From Ref. [2]).

7

Figure 1.4: Crystal-field splitting of 3d orbitals under cubic, tetragonal, and or-thorhombic symmetries (From Ref. [2]).

of holes per CuO2 plane, x, is a convenient parameter that can be used to com-

pare properties of cuprates belonging to different families. The undoped parent

compounds are Mott insulators with long-range antiferromagnetic (AF) order at

low temperature. As the doping increases above 5%, a well-known superconduct-

ing dome shows up with a maximum Tc at a doping level around 0.16. This is a

generic feature of all of the cuprates studied thus far and can be approximately

fitted to a a parabolic curve [3, 4]:

Tc/Tc,max = 1 − 82.6(x − 0.16)2 (1.1)

However, this is not a perfect fitting for YBCO due to a distinct 60 K phase [5].

Above the dome, there are three normal state regions: the pseudogap region, a

non-Fermi-liquid (strange metal) region and a Fermi liquid region. A lot of work

has been done on the pseudogap region but the results of different experiments

8

are in conflict. Basically there are two different scenarios. One is the so-called

“pre-formed” pair scenario. In this scenario, the pseudogap is closely related

to the superconducting gap and its onset temperature, T∗, will merge with the

superconducting transition temperature Tc in the overdoped region. Although

Cooper pairs are pre-formed at T∗, there is no global superconductivity due to

large phase fluctuations. Only at a temperature Tc where phase coherence is es-

tablished does the superconducting state develop. Angle-resolved photoemission

spectroscopy (ARPES) measurements [6, 7] show that the symmetry of the pseu-

dogap is the same as that of the superconducting state and the onset temperature

T∗ approaches the superconducting transition temperature Tc at optimal doping.

This is clear evidence that the pseudogap and the superconducting gap are closely

related to each other. Tunnelling spectroscopy [8] shows that both the pseudogap

and the superconducting gap scale in the same way as the doping changes and T∗

merges with Tc on the overdoped side.

In the second scenario the pseudogap state is viewed as an independent state

or even as a state competing with the superconducting state. In this case, T ∗ in-

tersects the superconducting dome and drops to zero at a quantum critical point

inside the dome. Experiments show that there are two different energy gaps in

k-space, one in the nodal region at the Fermi surface and the other one in the

antinodal regions, corresponding to the superconducting gap and the pseudogap,

respectively [9, 10, 11, 12]. As the doping decreases in the underdoped region, the

superconducting gap scales with TC while the pseudogap increases significantly.

Theories of this scenario usually involve one or more distinct ordering phenom-

ena such as charge density waves (CDWs), spin density waves (SDWs) or orbital

current order. This scenario has also been supported by experimental results ob-

tained with a variety of techniques including neutron scattering [13, 14], scanning

9

tunnelling microscopy (STM) [15, 16] and Nernst effect measurements [17, 18].

In addition, there is evidence that these two scenarios could be combined such

that there are two pseudogaps: one opening up at a high temperature, T∗, and

the other opening at a lower temperature, Tpair [19].

1.4 Quantum phase transition

As shown in the generic phase diagram (Figure 1.5), there might be four quantum

critical points(QCPs). From the parent compound, as the doping increases, one

first reaches the boundary between the AF insulating state and the pseudogap

state. The next boundary is the point where superconductivity develops. It

has been argued that these two points can be combined into one [21]. Thus

one will have a superconductor-(AF)insulator transition. In this scenario, there

will be no gap between these two states at zero temperature although at high

temperature there is a pseudogap state. The next critical point would be under the

superconducting dome if one believes the second scenario of pseudogap to be true.

Finally there is the point at which superconductivity disappears. Among all these

quantum critical points, the one under the dome is obscured by superconductivity

while the others can be studied directly using transport measurements.

It is believed that the superconductor-insulator transition at zero temperature

is an example of a quantum phase transition induced by varying a parameter of

the Hamiltonian of the system [22, 23]. Possible parameters include film thick-

ness [24, 25], magnetic field [26, 27, 28], carrier concentration [29], etc. A distinct

feature of QPTs is the success of finite size scaling analysis of electrical transport

data. A d-dimensional quantum system at finite temperature can be viewed as a

(d+1)-dimensional classical system when the dynamic exponent z=1 [22]. Near a

10

Figure 1.5: Generic phase diagram of the cuprates. Adapted from Ref [20].

11

quantum critical point both the spacial and temporal correlation lengths diverge

as a function of deviation of the tuning parameter from the critical point:

ξ ∝ δ−ν , ξt ∝ ξz

where ξ is the spatial correlation length, ξt is the temporal correlation length and

δ = |K−Kc| is the deviation of the tuning parameter from its value at the critical

point. K is the control parameter (thickness,magnetic field, carrier concentration,

etc.) and Kc is its critical value. The correlation length exponent ν and the

dynamical critical exponent z determine the universality class of the transition.

In a 2D system, the resistance near a quantum critical point collapses onto a

single scaling function R = Rcf(δT−1/νz), where Rc is the critical resistance [30,

31, 32, 33]. Thus by analyzing the transport data one can find Rc and νz and the

properties of SI transitions can be studied.

1.5 Motivation and outline

Since cuprates are ceramic compounds with a layered structure, their thicknesses

cannot be varied continuously. Previous studies [34, 35, 36] on films of different

thicknesses found superconductor to insulator transitions at low temperature as

the thickness was decreased. However detailed analysis was difficult as films of dif-

ferent thicknesses may have very different disorder and even different structures.

Moreover, there is a thickness threshold below which films are always insulating

possibly due to the mismatch of the lattice constant to the substrate lattice con-

stant. Magnetic field is another possible tuning parameter for the superconductor-

insulator transition, but for high-TC cuprates this is not easy to use, since the

upper critical field Hc2 is huge, usually more than 100 T.

12

Consequently, tuning carrier concentration would be the most practical ap-

proach for high-TC cuprates. There are two ways to do this, by chemical doping

or by electrostatically charging. The disadvantage of the former is that it can in-

troduce structural and chemical disorder and cannot be tuned continuously [37].

On the other hand, electrostatic charging is promising since it keeps the structure

fixed and is continuous and reversible [38, 39, 40, 41]. Moreover, a large effect

is expected in high-TC cuprates due to their much lower carrier concentrations

compared with those of conventional metals.

The main objective of this research was to study the superconductor-insulator

transition in high-TC cuprates using electrostatic charging, which can be carried

out using a field-effect-transistor(FET)-like devices to modulate carrier concen-

tration. Charge accumulation or depletion is restricted by the Thomas-Fermi

screening length, which is typically several Angstroms in the cuprates. The thick-

ness of one unit cell (UC) YBCO is about 11 Angstroms. Thus one needs ultrathin

films in which the active layer is only 1 or 2 UCs in thickness. There are a lot of

challenges in growing such thin YBCO films especially because of their sensitivity

to changes in chemical properties. These are described in Chapter 2 along with

film growth methods and film characterization techniques.

The other important parameter of a field effect transistor is the dielectric

constant of the gate insulator. To achieve observable carrier density changes in

high TC cuprates one has to use materials with very high dielectric constants.

SrTiO3 (STO) is a good candidate due to its high dielectric constant (especially

at low temperature) and the fact that it is epitaxially compatible with YBCO.

However, previous electrostatic charging experiments on high-TC cuprates using

STO as dielectric showed only small changes in TC [42, 43, 44] suggesting that

the situation is more complicated.

13

Another candidate is the so-called ionic liquid, which has been proved to have

the ability to induce very high carrier concentration changes up to 8×1014 cm−2 in

materials such as ZrNCl, STO, ZnO and YBCO [45, 46, 47, 48]. Such high carrier

concentrations are sufficient to tune the superconductor-insulator transitions in

high-Tc cuprates. While superconductivity was induced in ZrNCl and STO sam-

ples and a Tc shift of 50K was observed in a 10 UC YBCO films, no continuous

transition from superconductor to insulator has been found in YBCO. The reason

is that films as thin as 10 UC are still too thick. Due to the small Thomas-Fermi

screening length only one UC will be affected by gating. In a thick sample, the

proximity effect will dominate and no transition will be seen. In a recent paper,

Bollinger et al. reported a SI transition in La2−xSrxCuO4(LSCO) using an ionic

liquid as the dielectric [49]. Compared to LSCO, YBCO has a different crystal

structure and different chemical disorder which has important consequences.

To use an ionic liquid as a dielectric, special care is necessary, since ionic

liquids are liquids at room temperature. In addition they may undergo chemical

reactions with YBCO. In Chapter 3 the development of field effect devices using

both STO and ionic liquids as dielectrics is discussed.

In Chapter 4 experimental set-ups are described and the results are shown

and discussed as well. While gating using STO induces only small TC shifts, a

clear transition between superconducting and insulating behavior was realized in

a 7 UC thick YBCO film using an ionic liquid as a dielectric. By means of a

scaling analysis of different R(T) curves, the existence of a quantum critical point

was inferred at the boundary between insulating and superconducting regions and

the critical exponent product was deduced and compared with results from other

systems.

Finally conclusions and some future directions are presented in Chapter 5.

Chapter 2

Sample preparation and

characterization

Ultrathin YBCO films were deposited on (001) oriented STO substrates using

a high pressure oxygen sputtering system. Previous work has shown that this

technique can provide high quality epitaxial YBCO films [50, 51].

2.1 Substrate treatment

Strontium titanate crystals were used as substrates since they have a cubic struc-

ture at room temperature and their lattice constants (a=b=c=3.905 A) are close

to those of YBCO (a=3.82 A and b=3.89 A). YBCO films are very sensitive

and react with most chemicals at room temperature including H2O and CO2 in

air. This is a serious problem especially for ultrathin films so one should avoid

using photolithographic techniques in processing after film growth. Instead, well-

patterned amorphous Al2O3 films were deposited beforehand as masks. The area

covered with Al2O3 will then have an amorphous YBCO film on it, which is an

14

15

insulator. The uncovered area will then have an epitaxial YBCO film on it.

A typical commercial STO substrate has two kinds of terminations randomly

distributed on its surface, TiO2 and SrO2. To obtain high-quality YBCO films,

I removed the SrO2 endings and reduced the surface roughness. Inspired by the

work of Kawasaki et al. [52] and Koster et al.’s [53], I used a Hydrofluoric acid

(HF) solution to etch and clean the STO substrates. First, I put STO in de-ionized

water and sonicated for 20 minutes. The SrO2 on the surface reacts with water

to form Sr(OH)2 while TiO2 is quite stable. Then I dipped the substrate into

a 10:1 buffered oxide etch (BOE), an aqueous NH4-HF solution, for 20 seconds.

This was followed by rinses with de-ionized water. This process remove the SrO2

endings. Finally, the BOE etched substrate was annealed in an O2/O3 mixture

for 6 hours at 750 oC to achieve a smooth surface. Figure 2.1 shows typical AFM

images of a STO substrate before and after treatment.

2.2 Film deposition using a high pressure oxy-

gen sputtering system

Yttrium Barium Copper Oxide films were deposited in a high pressure oxygen

sputtering system using a commercial YBCO target (2.0 inches in diameter). The

system was pumped down to a base pressure of 1.0×10−6 mbar. Strontium titanate

substrates were heated to 900oC at an oxygen pressure of 0.6 mbar. Plasma

ignition took place at a voltage of about 480 V, whereupon the discharge current

increased to 200 mA. During this process, the oxygen pressure was increased to

2.0 mbar alternately with increases in the discharge current. Then we waited

while the system pre-sputtered for about 1 hour. After pre-sputtering the plasma

voltage was about 240 V. During deposition this voltage dropped to about 230

16

Figure 2.1: AFM images of a STO substrate before (top panel) and after (bottompanel) treatment.

17

V. We carefully adjusted the target-substrate distance to make sure the substrate

was in the boundary region of the oxygen plasma. The deposition rate was about

1 nm/minute. After deposition, samples were cooled down to 600oC in 800 mbar

oxygen at a rate of 10 oC/minute. The film was annealed at this temperature for

30 minutes to 90 minutes, and then cooled down to room temperature naturally.

2.3 Film characterization

Films were characterized using high resolution X-ray diffraction (XRD). In Fig-

ure 2.2, the XRD patterns of films of different thicknesses are compared. The

presence of only (00l) peaks of YBCO and STO indicates that these films have

no impurity phases and they are perfectly oriented with the c-axis perpendicular

to the substrate surface. For films thinner than 7 nm, the peaks are broadened

and the intensities are lowered. Considering the lattice mismatch of YBCO with

STO (Ma/a∼2.2% and Mb/a∼0.4%), the first several unit cells will be strained

and their structures will be different from the bulk structure.

Typical rocking curves are shown in Figures 2.3 and 2.4. The full width at

half maximum (FWHM) values are quite small (0.07 o-0.08 o), which indicates

these films are of high quality with all of the atomic layers parallel to each other

and to the substrate surface.

Film thicknesses were measured using X-ray reflectivity and the results are

shown in Figure 2.5. The high angle part shows the first Bragg peak and its

behavior is similar to that of the wide angle XRD data. The low angle part can

be fit using software called GenX [54] to get information about film thickness

and film roughness. A comparison of raw data with fitted curves is shown in

Figure 2.6. The interface roughness for all of the films studied was about 5 A.

18

A typical resistance vs. temperature curve for a 15 unit cell film is shown

in Figure 2.7. The sample was measured right after deposition using a van der

Pauw configuration. Contact was made using Indium dots on the corners. The

superconducting transition is quite sharp with an onset temperature greater than

90 K. The temperature dependence of the resistance above TC is linear and can

be extrapolated to zero (dash line). This indicates that the stoichiometry of the

target is good and that the growth conditions have been optimized.

19

Figure 2.2: X-ray diffraction patterns of YBCO films of different thicknesses. Filmthicknesses from top to bottom: 12.5 nm, 9.5 nm, 8.0 nm, 7.0 nm, 6.0 nm, 5.5 nmand 5.0 nm.

20

Figure 2.3: Rocking curve of the (005) peak of a 5.5 nm thick YBCO film.

21

Figure 2.4: Rocking curve of the (005) peak of an 8 nm thick YBCO film.

22

Figure 2.5: X-ray reflectivity data of films of different thicknesses. From top tobottom: 13.5 nm, 12.5 nm, 11 nm, 10.5 nm, 9.5 nm, 8.5 nm, 8.0 nm, 7.0 nm, 6.0nm, 5.5 nm and 5.0 nm.

23

Figure 2.6: Comparison of X-ray reflectivity raw data (black) with fittedcurves(red).

24

Figure 2.7: Typical resistance vs. temperature curve of a 15 UC thick YBCOsample measured using a van der Pauw configuration immediately after deposition.

Chapter 3

Field effect device development

3.1 Introduction

The number of induced carriers in a field effect transistor is determined from the

following equation:

n2d =

∫ VG

0

ε0εrV

eddV, VG < Ebd. (3.1)

where n2d is the 2D carrier concentration, ε0 is the dielectric constant of vacuum,

εr is the dielectric constant of the gate insulator, VG is the gate voltage, e is the

electron charge, d is the thickness of the gate insulator and Eb is the breakdown

electric field. Traditional semiconductor-based FET devices use SiO2 as the gate

insulator. This has a dielectric constant of 3.9 at room temperature and can

induce carrier density changes of 1012 − 1013 cm−2 with a gate voltage of several

volts. However, the carrier concentration of high-TC cuprates is at the level of

1014 cm−2, which is one order of magnitude higher than what a traditional FET

device can achieve. In order to increase the carrier concentration, one has to use

a gate material with a higher dielectric constant. Also a large breakdown electric

field and a small thickness are both necessary.

25

26

3.2 Properties of SrTiO3

SrTiO3 (STO) was expected to be a promising gate insulator for high-Tc cuprates

and other transition metal oxides due to its high dielectric constant and close

lattice match to these materials. The dielectric constant of STO is about 300 at

room temperature and increases as temperature drops. At T > 100K, it follows

a Curie-Weiss law, εr ∝ (T − Tc)−1, where Tc ≈ 38K is the predicted ferroelectric

transition temperature [55]. Usually, a ferroelectric will lose its intrinsic polar-

ization at the ferroelectric transition temperature TC and become a paraelectric.

This is similar to a ferromagnetic material to lose its spontaneous magnetization

at the Curie temperature and become paramagnetic [56]. The electrical suscep-

tibility, χ, follows the law χ = A/(T − TC) (A is a constant), which has the same

form as the Curie-Weiss law of magnetic susceptibility. However, the ferroelectric

transition never happens since the quantum fluctuation amplitude of the Ti ion is

larger than its calculated ferroelectric displacement [57]. Instead, STO has been

referred to as a quantum paraelectric at low temperature and its dielectric con-

stant increases significantly at T < 10K and saturates at εr ∼ 20, 000 − 40, 000

below 4 K. Hemberger et al. [58] found that at high electric field (> 2kV/cm),

where the field induced displacement dominates the quantum fluctuations, there

is a peak in the εr(T ) curve indicating the recovery of ferroelectric state at low

temperature.

Another feature of STO is the so-called ”space charge” issue [59, 60, 61]. Upon

applying a dc gate voltage, excess negative space charge develops in STO. At room

temperature, the space charge distributes uniformly in bulk in tens of minutes due

to thermal diffusion. However, at low temperature the distribution process is very

slow, usually taking several days or longer. Thus the space charge is conserved

27

even after gate voltage is removed. A higher gate voltage will redistribute the

space charge in a nonuniform way and thus change the dielectric constant. By

measuring capacitance (or dielectric constant) vs. gate voltage one finds a hystere-

sis loop at low temperature. This is a significant problem for device development.

However, in laboratory experiments, one can always warm up the device to room

temperature, remove the gate voltage, short the circuit and wait until the space

charge redistributes.

3.3 Backside gating using SrTiO3 as a dielectric

material

In order to achieve high carrier transfers, one needs small dielectric thicknesses

according to Equation 3.1. One option is to use STO films with thicknesses as

small as several hundreds of nanometers [39, 62]. Thus a relatively small gate

voltage can produce a high electric field across the film. The dielectric constants

of thin films are lower than those of single crystals. At high electric fields, this

difference is not that significant [63]. The main disadvantage of using a thin film is

that the surface layer of STO is very rough after deposition. Thus it is very hard to

grow high quality ultrathin YBCO films on top of such surfaces. The alternative

is to use STO single crystals. A standard commercial STO single crystal has a

thickness of 300 µm and can be thinned to 50 µm using a bead-blasting technique.

The detailed thinning process is described in the thesis of Dr. Eblen-Zayas [64].

Samples thinner than 50 µm usually suffer from dimples or irreversible oxygen loss.

After thinning the backside is of bowl shape. A Pt gate electrode is deposited

on it before film growth. In order to have high quality ultra thin-YBCO films,

insulating PrBa2Cu3O7−x (PBCO) layers are usually deposited as buffer layers (in

28

between STO and YBCO) and capping layers (on top of YBCO).

Although the substrate is thinned to 50 µm, one still has to use a gate voltage

as high as 1000 V to produce a large enough charge transfers to the sample. Such

a high gate voltage requires a high vacuum environment and well-isolated wires.

Figure 3.1 shows a sketch of a STO-based FET device.

Figure 3.1: Sketch of a backside gated field effect transistor device. The STOsubstrate was thinned down to about 50µm. A patterned amorphous Al2O3 filmwas deposited to define the geometry before YBCO film growth. Pt electrodeswere deposited through a shadow mask.

29

3.4 Properties of the ionic liquid

Recently, ionic liquids have been used to make FET-like devices to induce carrier

concentration changes of 8 × 1014cm−2 or higher in materials such as ZrNCl,

STO, ZnO and YBCO [45, 46, 47, 48]. The properties of ionic liquids include

high thermal stability, non-volatility, non-flammability, low vapor pressure and

compatibility with most material systems. FET devices using ionic liquid as

dielectric are usually called electronic double layer transistors(EDLTs). Upon

applying a gate voltage, large cations or anions in the ionic liquid can move towards

the sample surface and carriers are induced in the sample accordingly, forming an

electric double layer (EDL). The cation (or anion) layer and induced carrier layer

are separated by distances of nanometer scale. Thus the effective capacitance is

1000 times larger than that of an usual semiconductor based device. A schematic

diagram of the configuration is shown in Figure 3.2.

The ionic liquid used here was N,N-diethyl-N-methyl-N-(2-methoxyethyl) am-

monium bis (trifluoromethanesulfonyl)-imide (DEME-TFSI), which has no clear

melting or freezing point but has a glass transition temperature around 182 K.

At 240 K, it condenses into a rubber-like state and most chemical reactions are

suppressed. Thus it is safe to change gate voltages at this temperature. In this

state, the ions are still mobile so a gate voltage will move ions towards the sample

surface and induce carriers in the sample. At temperature below 190 K, the ionic

liquid is frozen but the induced carriers will remain constant.

A capacitance-voltage curve measured at 240 K is shown in Figure 3.3. The

number of induced carriers was calculated by integrating the leakage-current

curves as shown in the inset of Figure 3.3. This method cannot provide accu-

rate results at high gate voltages due to the high background leakage current.

30

Figure 3.2: Cartoon of an ionic liquid base electronic double layer transistor(EDLT). Upon applying a positive gate voltage, cations (red circles) are electro-statically accumulated onto the sample surface and negative carriers are inducedinside the sample, forming an electric double layer (EDL). Adapted from Ref. [45].

31

However, the alternative AC method is not appropriate either due to the large

time constant. Thus the calculated carrier transfer cannot be used for quantitative

analysis.

3.5 Top gating using an ionic liquid as a dielec-

tric material

As described in Chapter 2, films were pre-patterned using amorphous Al2O3 as

masks. After deposition, 20 nm Pt films were sputtered onto the samples as

electrodes using a physical mask in the form of a Hall bar configuration. Here no

photolithography was involved since YBCO is very sensitive. No capping layers

were deposited since the ionic liquid had to be put directly on top of the YBCO

films. A small glass tube was glued onto the sample surface using epoxy and a

sketch is shown in Figure 3.4. Ionic liquid was placed in the glass tube and a Pt

coil was used as gate electrode.

32

Figure 3.3: Capacitance-voltage curve of the ionic liquid (DEME-TFSI) at 240K.Inset: Leakage current vs. time after the gate voltage was changed at 240K.

33

Figure 3.4: Cartoon of the FET structure used to gate YBCO films (side view).A patterned amorphous Al2O3 film was deposited to define the geometry beforeYBCO film growth. This enabled us to avoid post-deposition patterning. Ptelectrodes were deposited through a shadow mask. The ionic liquid filled a smallglass tube glued on top of the structure.

Chapter 4

Experimental results and

discussion

4.1 Experimental set-up

All transport measurements were made using a Quantum DesignTM Physical Prop-

erties Measurement System (PPMS) employing external current sources and volt-

meters in a standard four-terminal configuration. The DC current source was a

KeithleyTM 6220. It was used to provide a measuring current of 10 nA or 100 nA.

KeithleyTM 182 and 2182 nanovoltmeters were used to measure voltages across a

sample. Gate voltages were provided using a KeithleyTM 487 voltage source or a

KeithleyTM 6517A electrometer. Leakage currents were measured with the inter-

nal current meters of these instruments. Labview was used to control all these

instruments.

34

35

4.1.1 Backside gating using SrTiO3 as a dielectric

For backside gating experiments a special sample holder was used in which the

gate wire was well isolated to support high gate voltages. In order to prevent

possible electrical breakdown at high voltage a high vacuum mode (< 1 mTorr)

was used during measurement. Samples were shorted at room temperature before

the original cool down. Gate voltages were changed at 2 K. Then samples were

warmed up to 120 K and resistance data was taken during warming up. Before

changing to the next gate voltage, samples were warmed up further to 300 K.

Then the gate voltage was removed and samples were shorted for 30 mins. This

process redistributes the space charge. The leakage current was kept below 1 nA

during measurement.

4.1.2 Top gating using an ionic liquid as a dielectric

A device like that described in Figure 3.4 was mounted onto a standard PPMS

sample puck. The ionic liquid (DEME-TFSI) condenses into a rubber-like state

at 240 K, a temperature at which most chemical reactions are suppressed. If the

device was kept at room temperature for several hours with ionic liquid on it, there

was an increase in sample resistance and a drop in TC , possibly due to chemical

reaction that irreversibly alters the film. However, after cooling down and being

kept below 240 K, no changes were seen over several days. In the measurements,

samples were quickly cooled down to below 240 K over several minutes after ionic

liquid was applied. The gate voltage was changed at 240 K where it was held for

about 1 hour before further cooling. The gate voltage was kept constant during

measurements and the leakage current was kept below 20 nA. A large leakage

current might bring about chemical degradation of the samples.

36

4.2 Results of backside gating using SrTiO3 as a

dielectric

PrBa2Cu3O7−x (PBCO) has the same structure as YBCO but it is an insulator.

Several possible models such as hole filling, localization, magnetic pair-breaking

and the role of hybridization have been proposed to explain this behavior but it is

still controversial [65]. Using PBCO as buffer layers and capping layers, YBCO

films as thin as 2 UC are superconducting. In backside gating experiments films

with thickness ranging from 2-4 UCs were studied. Typical backside gating results

are shown in Figure 4.1. For a 4 UC thick YBCO film, TC shifts by about 4 K

when VG is changed from +200 V to -500 V. Here TC is defined as the midpoint

of the transition. The bottom panel shows similar results for another 2 UC thick

YBCO film with a 2 UC insulating PBCO buffer layer. Here TC shifts only 5

K as VG was changed from 0 to -700 V. In both samples, the normal resistance

drops more than 20% with negative VG , indicating holes are being injected into

the samples. Figure 4.2 shows interesting results on a 3 UC YBCO film with 5

UC insulating PBCO capping layer. With negative VG (top panel), the normal

resistance drops and TC decreases. It appears that the film has been doped to the

overdoped side although the onset TC of the original sample is only 80 K and the

transition is quite broad. The bottom panel shows that with positive VG normal

resistance increases and TC drops, which indicates the film has been moved to

the underdoped side. Unfortunately, no superconductor-insulator transition was

observed even with VG as high as 1000 V.

The weakness of the above mentioned effects was surprising. The STO sub-

strates were etched to only 50 µm in the middle. Thus a gate voltage of 700 V will

produce a electric field larger than 100 kV/cm. The gate voltage was changed at

37

Figure 4.1: Top. Resistance vs. temperature for a backside gated 4 UC thickYBCO film with VG varying from +200 V to -700 V. This film has a 5 UC thickPBCO capping layer on top but no buffer layers. From +200 V to 0, VG waschanged in increments of 50 V. From 0 to -700 V, VG was changed in incrementsof -100 V. Bottom. Resistance vs. temperature for a backside gated 2 UC thickYBCO film with VG varying from 0 to -700 V. This film had a 2 UC thick PBCOcapping layer and 2 UC thick PBCO buffer layer. VG was changed in incrementsof -100 V.

38

Figure 4.2: Resistance vs. temperature for a backside gated 3 UC thick YBCOfilm. This film had a 5 UC thick PBCO capping layer but no buffer layer. Top.VG ranging from 0 to -999 V. Bottom. VG ranging from 0 to 999 V.

39

2 K. At this low temperature STO has a large dielectric constant and the induced

carrier concentration approaches 7 × 1013cm−2 as calculated using Equation. 3.1.

Assuming the induced carriers are doped onto CuO2 planes, a simple calculation

based on the lattice constants (3.82 A × 3.89 A × 11.68 A) shows that a carrier

concentration of 7 × 1013 cm−2 corresponds to 0.1 holes/Cu (there are two CuO2

planes per unit cell in YBCO). Since 0.16 holes/Cu is the optimal doping point,

a doping level change of 0.1 holes/Cu should induce a large TC shift or even a

superconductor-insulator transition in these YBCO films. However it did not.

Similar results have been reported by Salluzzo et al. ( [66]) for STO/NdBa2Cu3O7

samples. They could not induce any SI transition in 3 UC or 4 UC films even

with VG =±900 V. These results indicate the mechanism of electrostatic doping

in YBCO is very different from what was expected. In Ref. [66], they carried out

X-ray absorption spectroscopy studies and found that the induced carriers are

doped onto the CuOx chains while only a small fraction are transferred to the

CuO2 planes. Simulation [67] shows that in case of TiO2-terminated substrate,

the interface is a stack of ...SrO/TiO2/BaO/CuO2/Y/CuO2/...layers and the in-

duced carriers will be distributed mostly on TiO2 (48%) and BaO (25%) layers

while only 5% carriers are doped onto CuO2 planes. Since TC is determined by

the carrier concentration on the CuO2 planes, a much higher change in the carrier

concentration is required to induce a SI transition in YBCO.

40

4.3 Results of top gating using an ionic liquid as

a dielectric

4.3.1 Samples of different thicknesses

A series of ultrathin YBCO films of different thicknesses were grown in the high

pressure oxygen sputtering system and measured using standard four-terminal

techniques. Films thinner than or equal to 6 UC were insulating whereas thicker

ones were superconducting. Films were deposited directly onto STO substrates

without any buffer layer. In a previous unpublished work [68] Javier Garcia-

Barriocanal et al. studied YBCO/STO superlattices grown by high pressure oxy-

gen sputtering using electronic transport and scanning transmission microscopy

measurements. It was found that single or two unit cell steps at the STO in-

terface cause alterations of the stacking sequence of the intra-cell YBCO atomic

layers. The steps in the STO surface create stacking faults that give rise to anti-

phase boundaries which break the continuity of the CuO2 planes and suppress

superconductivity. It is reasonable to think that the 5 to 6 unit cell dead layers

can be related to the same chemical disorder produced at the interface with the

substrate. Furthermore, it has been reported similar alterations of the interfa-

cial chemistry and structure of cuprates grown by other techniques such as MBE

(see Ref. [49] supplementary information, and references within). All films were

deposited under the same conditions which were optimized to yield the highest

TC ’s for thick films. No capping layers were deposited since the ionic liquid was

on top of the film. Consequently, it is very easy for ultrathin YBCO films to lose

oxygen. For superconducting films with thickness ranging from 7 UC to 10 UC,

the transition is broadened and TC is lowered due to oxygen loss. There was no

41

simple relationship between TC and film thickness but this will not change our

conclusions.

Figure 4.3 shows the resistance vs. temperature curves for a 6 UC thick YBCO

film. The original film is an insulator. With negative gate voltage the normal

resistance drops and a small dip develops at low temperature. This dip is a

signature of local superconductivity which indicates holes have been injected into

the film. As VG is increased to -2.0 V there is a big drop in the normal resistance

and the R(T) curve exhibits a global superconducting transition with TonC close to

30 K. Here TonC is taken to be the temperature at which the sheet resistance falls

to 90% of its normal value. After -2.3 V, VG was changed in -0.01 V increments

until the leakage current exceeded the limit (20 nA) and TonC increased to a value

larger than 50 K.

Shown in Figure 4.4 is the result for an 8 UC thick YBCO film. The original

sample was superconducting with TonC close to 65 K. With a positive gate volt-

age, the normal resistance increases and the transition temperature drops, which

indicates that holes are depleted. An interesting feature is that as VG increases,

a kink develops at low temperature. This kink evolves into a dip at high values

of VG and one can define another transition temperature T2 corresponding to the

onset transition temperature T1. As VG changes to -1.0 V, insulating behavior

can be seen at the lowest temperature but at high temperature there is still a

sharp drop around T1 and this drop persists to VG =2.5 V where the leakage

current exceeds the limit (20 nA).

At first sight, it seems there are two phase transitions possibly caused by

inhomogeneity in the film . In this case, different parts with different transition

temperatures are connected in series. When holes are depleted in the sample

both T1 and T2 should move to lower temperatures. However, we notice that

42

in Figure 4.4, although T2 has dropped more than 30 K under negative VG , T1

changes only by several Kelvin and even saturates at high VG . Since films thinner

than or equal to 6 UC were insulating, a 8 UC thick film might have only 2 or 3

superconducting unit cell layers. The field effect can affect only a single UC due

to the small Thomas-Fermi screening length (several A). While holes in the top

layer have been depleted, the layer underneath is not affected by much. At high

temperatures, the top layer is in a metal-like state. For metal/supercondcutor

bilayers, the proximity effect will dominate thus there is a sharp drop in the

normal resistance at T1. At lower temperatures, the top layer turns out to be

an insulator under higher negative VG . For insulator/superconductor bilayers,

the proximity effect will be suppressed thus one would expect insulating behavior

at the lowest temperatures. Moreover, some part of the underlayer might also

be affected at high values of VG . Thus the superconducting transition in the

underlayer is broadened. This means at low temperatures the underlayer is not

that superconducting any more and the proximity effect will be suppressed further.

Thus more insulating behaviors would be expected.

Results for a 10 UC film are shown in Figure 4.5. With positive VG , the

normal resistance increases and transition temperature TmidC drops. Here Tmid

C is

a temperature at which the sheet resistance falls to 50% of its normal value.

However, as VG increases to a value larger than 2.5 V, both the normal resistance

and TmidC saturate. Another feature is that during the charging process Ton

C does

not shift much as compared to TmidC . These results confirm the assumption that

only the top layer can be affected by the field effect whereas the underlayers are

hardly affected. In a thick film, there are many unit cell thick layers that are

superconducting. Thus the proximity effect is quite strong even at the lowest

temperatures. In order to study the SI transition one has to grow films with

43

active layers only 1-2 UC in thickness.

In Section 4.3.2 the data for a 7 UC thick film will be presented in detail. The

original film was a superconductor with an onset transition temperature close to

77 K. With a negative VG , a clear evolution from superconductor to insulator

was observed. This is different from the behavior of both the 8 and 10 UC thick

films, in which their onset transition temperatures did not change by much. Under

electrostatic doping, the 7 UC thick film showed an obvious change of TonC with

negative VG . This is a strong evidence that a nominal 7 UC thick film has only

a 1 UC thick active layer and that the field effect can only affect the top layer.

4.3.2 The evolution from superconductor to insulator in a

7 UC thick sample

Resistance vs temperature curves at various gate voltages of a 7 UC thick YBCO

film are shown in Figure 4.6. The sample starts out as a superconductor with

TonC ∼ 77K. Here Ton

C is taken to be the temperature at which the sheet resistance

falls to 90% of its normal value. An insulator is realized at a gate voltage of only

1.52 V. Here TonC is a nonlinear function of VG . There is a VG threshold of about

0.3 V below which almost no change in the transition temperature or normal

resistance is seen. Then TonC drops by about 30 K as VG increases from 0.5 to 1.1

V, which is about 5 K/0.1 V. However, as VG increases from 1.1 to 1.25 V, a change

of 0.2 to 0.3 V can induce a TonC shift of about 5 K. This nonlinearity suggests that

the gate voltage cannot be used as a tuning parameter for quantitative analysis.

As VG increases to 1.37 V, the curves of R (T ) flatten out at the lowest tem-

perature and then undergo a small upturn at VG =1.40 V although they initially

decrease as temperature decreases. Finally R (T ) evolves to an insulating state

44

Figure 4.3: Sheet resistance (Rs) vs. temperature of a 6 UC thick YBCO filmwith the gate voltage varying from 0 to -2.3 V. From top to bottom: VG =0, -0.3,-0.6, -1.0, -1.2, -1.5, -1.8, -2.0, -2.3, -2.31, -2.32, -2.33, -2.34, -2.35, -2.36 (V).

45

Figure 4.4: Rs(T) curves of a 8 UC thick YBCO film with the gate voltage varyingfrom 0 to 2.5 V. From bottom to top: VG =0, 0.5, 0.8, 1.0, 1.1, 1.2, 1.22, 1.24,1.26, 1.28, 1.3, 1.5, 1.8, 2.0, 2.3, 2.5 V.

46

Figure 4.5: Sheet resistance vs. temperature curves for a 10 UC thick YBCO filmwith the gate voltage varying from 0 to 5.0 V. From bottom to top: VG =0, 1.0,2.0, 2.2, 2.5, 2.7, 3.0, 4.0, 5.0 (V).

47

Figure 4.6: Logarithm of the sheet resistance vs temperature for a 7 UC thickYBCO film with the gate voltage varying from 0 to 1.52 V. From bottom to top:0, 0.3, 0.5, 0.7, 0.8, 0.9, 1, 1.1, 1.12, 1.14, 1.17, 1.20, 1.25, 1.27, 1.30, 1.33, 1.35,1.37, 1.40, 1.43, 1.44, 1.46, 1.48, 1.50, 1.52 (V). Inset: enlarged low temperatureregime near the transition from the superconducting to the insulating regimes.

48

as VG increases further, as can be seen clearly in the inset of Figure 4.6. Interest-

ingly, the resistance on the insulating side up to VG =1.48V is thermally activated

with an Arrhenius type R (T ) relation. Above this gate voltage the logarithm of

the sheet resistance is fit by a T−1/3 dependence consistent with 2D Mott variable

range hopping.

The low temperature upturn is similar to that observed in amorphous MoGe

films and granular superconductors [28, 69, 70, 71, 72] and will dramatically affect

any quantitative scaling analysis. This might be an evidence of a mixed phase

separating the superconducting and insulating regimes. Nevertheless, the thick-

ness fluctuations in the single unit cell active layer could also contribute to this

upturn. It is also possible that there is a superconducting underlayer that is not

completely depleted.

For further quantitative analysis of the data, one needs the induced carrier

concentration. As discussed above, the gate voltage is not simply related to the

carrier concentration and the Hall resistance cannot be used because of the com-

plicated electronic properties of YBCO. One approach is to assume that Drude

behavior is appropriate at high temperatures and take 1/Rs(200K) to be propor-

tional to the carrier concentration measured as carriers per in-plane Cu atom.

Comparing this with the carriers per in-plane Cu atom derived from the phase

diagram of bulk YBCO [73], they match with a constant coefficient of 0.165 as

plotted in Figure 4.7. This is especially true in the transition regime which is the

focus of quantitative analysis.

Using the measured R (T ) curves and the calculated carrier concentrations, a

phase diagram can be constructed and is plotted as Figure 4.8. It is similar to

the phase diagram of bulk high-Tc cuprates derived from chemical doping. With

electrostatic doping it is measured continuously and perhaps more accurately,

49

Figure 4.7: Carrier concentration calculated using 0.165/Rs(200K) (red dots) com-pared with that derived from the phase diagram of bulk high-Tc cuprates (blacksquares). The bulk phase diagram was adapted from Ref. [73]. The inset showshow the carrier concentration was determined from the bulk phase diagram usingmeasured values of Ton

C at different gate voltages.

50

Figure 4.8: Color plot of the resistance vs temperature and calculated carrierconcentration. This can be interpreted as a phase diagram. Different colorsrepresent different sheet resistances. The dash line is Ton

C . The white area in thebottom left hand corner is a regime in which the I-V curves were nonlinear.

51

especially in the transition and insulating regimes. The data plotted here are in

the linear regime of the I-V curves. There are nonlinear I-V curves deep in the

insulating regime which are denoted by white in the figure.

4.3.3 Quantum phase transition

It is believed that the superconductor-insulator (SI) transitions in high-Tc cuprates

at zero temperature is an example of a quantum phase transition (QPT) [22, 23].

A signature of a QPT at nonzero temperature is the success of finite size scal-

ing in describing the data [74, 28, 29]. Basically, the resistance of a 2D sys-

tem near a quantum critical point (QCP) collapses onto a single scaling function

R = Rcf(δT−1/νz), where RC is the critical resistance, δ is tuning parameter, T is

the temperature, ν is the correlation length critical exponent and z is the dynamic

critical exponent [30, 31, 32, 33].

When a QCP is approached, resistance isotherms as a function of the carrier

concentration x should cross at the critical resistance RC and all resistance data

should collapse onto a single scaling function. Figure 4.9 shows isotherms from

2K to 22K. A clean crossing point can be seen if the lowest temperature isotherms

are neglected. The critical resistance per square is about 6.0 kΩ, which is very

close to the quantum resistance given by RQ = h/(2e)2 = 6.45kΩ considering

that imprecise shadow masks were used to define the four-terminal configuration.

The critical carrier concentration is xc=0.048±0.0005 carriers/Cu, close to that

derived from the bulk phase diagram (0.05). But this is not surprising given that

the bulk phase diagram was used to calibrate the carrier concentration.

The results of the finite size scaling analysis are shown in the inset of Figure 4.9.

All the sheet resistance data from 6K to 22 K collapse onto a single function

Rs = Rcf(|x−xc|T−1/νz) if νz = 2.25±0.05. Assuming z=1.0 [75], the value ν =

52

Figure 4.9: Isotherms of R (x) at temperatures ranging from 2 K to 22 K.The carrier concentration x is calculated using the phenomenological relationx=0.165/Rs(200K). The arrow indicates the crossing point where RC =6.0kΩ and xc=0.048±0.0005 carriers/Cu. Inset: Finite size scaling analysis ofR (T ) for data in the range from 6 K to 22 K. The calculated carrier concen-tration x=0.165/Rs(200K) was used as the tuning parameter. The best collapsewas found when νz = 2.25 ± 0.05.

53

2.25± 0.05 is close to that of the universality class of a metal-insulator transition

in an anisotropic 2D system (7/3) [76] or that of the quantum percolation model

(2.43) [77]. Previous studies of QPTs in amorphous bismuth [29] and STO [78]

found νz ≈ 0.7, which is compatible with (2+1)D-XY model. In amorphous MoGe

films [28, 74] νz ≈ 1.3, which is consistent with classical percolation theory. The

value of νz = 2.25±0.05 for YBCO is different from νz = 1.5 found for LSCO [49].

This could be a consequence of the difference in disorder of the two systems. Also

the scaling of the YBCO data breaks down below 6 K, which is a consequence of

the nonmonotonic behavior of R (T ) at low temperature at gate voltages in the

transition regime. The data for LSCO are all above 4.2 K and may not extend

to low enough temperature to observe the breakdown of scaling. These results

suggest that the transition from superconductor to insulator is indirect and may

involve an intermediate phase and possibly multiple QCPs. Furthermore, this

transition between superconductor and insulator is different from the QPT inside

the superconducting dome suggested to give rise to the anomalous behavior of

underdoped cuprates [79].

4.3.4 Quantum critical behavior in the presence of mag-

netic field

Transport measurements were also carried out for the 7 UC thick film in a 9

T magnetic field and the results are shown in Figure 4.10. The magnetic field

was applied at 2 K after cooling down from 240 K in zero magnetic field (ZFC).

The resistance vs. temperature curves show a clean superconductor-insulator

transition as the gate voltages changes from 0 to 1.52 V. Compared to the R(T)

curves shown in Figure 4.6, there are no upturns at the low temperature part on

54

the superconducting side. One hypothesis is that those upturns might come from

the local superconducting islands or underlayers and now they are suppressed by

the magnetic field. Thus we have a cleaner SI transition and there is no mixed

regime in between the superconducting and insulating regimes.

The carrier concentration was calculated the same way as was down in Fig-

ure 4.7 (x=0.165/Rs(200K)) and the sheet resistance in zero magnetic field was

used assuming that the magnetic field does not change the doping level. The

isotherms from 2 K to 22 K are shown in Figure 4.11 and a clean crossing point

can be seen including the lowest temperature curves. The critical carrier concen-

tration is xc=0.055±0.0005 holes/Cu, larger than the one found in zero magnetic

field (0.048±0.0005 holes/Cu) and the critical sheet resistance is 4.5 kΩ, smaller

that the quantum resistance for pairs(6.45 kΩ). The inset of Figure 4.11 shows

the finite size scaling analysis. All the sheet resistance data from 2 K to 22 K

collapse onto a single function Rs = Rcf(|x − xc|T−1/νz) with νz = 2.25 ± 0.05,

the same as the one found in zero magnetic field.

Two scenarios have been proposed to explain the SI quantum phase transi-

tion [23]. One is the fermionic scenario, in which the SI transition is driven by

amplitude fluctuations. On the superconducting side there are condensed Cooper

pairs while on the insulating side, the Cooper pairs are broken and electrons are

localized. The other scenario is the bosonic picture [33]. In this scenario, on the

superconducting side, the Cooper pairs are condensed to support superconduc-

tivity while the vortices are localized. On the insulating side, the vortices are

mobile while the Cooper pairs are localized (Bose insulator) [27]. Note that in

the bosonic scenario, the fermionic excitations, i.e., the unpaired electrons, are

neglected.

As discussed before, our results in zero magnetic field are consistent with the

55

bosonic scenario. In particular if one consider the duality between the Cooper

pairs and the vortices, then Rc is exactly h/(2e)2Ω = 6.45kΩ and we have a very

close value Rc = 6.0kΩ. The critical exponent product (νz = 2.25 ± 0.05) is

consistent with the quantum percolation theory [77] and has been seen in highly

disordered InOx films [80].

In the presence of magnetic field, the bosonic scenario changes a little in the

sense that the vortices, which used to be vortex-antivortex pairs in zero mag-

netic field, are now field induced vortices if H > Hc1. On the superconducting

side, the induced vortices are still localized due to disorder and repulsive interac-

tions [32], forming a vortex glass. On the insulating side, the Cooper pairs are

localized while the vortices, unpaired or field induced, are both mobile. As the

magnetic field increases, more induced vortices will drive the system to be more

Bose-insulating [80]. This makes it easier to tune a superconducting film to the

Bose-insulating state. Thus the SI transition can take place at a higher carrier

concentration. The scaling analysis indicates that it is still a quantum phase

transition and the bosonic scenario still applies.

The product of the critical exponents (νz = 2.25±0.05) remains the same in the

presence of magnetic field. Similar results have been reported before in thickness-

driven SI transition in a-Bi films [81], where the critical exponent product was

found to be independent of the magnetic field and close to that obtained in zero

magnetic field. This means the universality class of the SI transition might not

be changed by a relatively weak magnetic field.

However, in our data the critical resistance drops to 4.5 kΩ in the presence of

magnetic field. We can rule out the contribution from the fermionic excitations,

although in high magnetic fields, Cooper pairs might be broken and the unpaired

electrons will contribute to the conductivity. This feature has been reported by

56

Yazdani et al. [28] in magnetic-field-tuned a-MoGe films, in which the critical

resistance drops significantly due to the contribution from fermionic excitations

near the SI transition. A two-fluid model was used to estimate the conduction:

σ = σf + σb, where σf is from the unpaired electrons and σb is from the bosons.

In our case, Rc = Rb/(1 + Rb/Rf) = 4.5 kΩ. Rb is the critical resistance from

the bosonic contribution and we can use the value in zero field (6.0 kΩ) since the

bosonic scenario apparently applies. Thus Rf = 18 kΩ is the contribution from

the unpaired electrons. Since Rf and Rb are of the same order and they cannot

necessarily follow the same scaling function as the carrier concentration changes,

then the scaling should have failed. However, our data (Figure 4.11) collapse

onto a single function and the critical exponent product does not change in the

presence of magnetic field, which means the fermionic contribution should not be

taken into account. For high-TC cuprates, this is not surprising since the upper

critical field (Hc2) is very high and 9 T magnetic field might not be high enough

to break the Cooper pairs.

On the other hand, the duality picture is not perfect since the Cooper pairs in-

teract as 1/r (Coulomb interaction) and vortices interact logarithmically [33].Thus

the critical resistance should not be universal and should depend on the nature of

the interactions [23]. In the presence of magnetic field, the local superconducting

islands will be suppressed and the Cooper pairs will have a more homogeneous

background and their interaction might be changed and the vortex-vortex inter-

action might also be changed by the presence of magnetic field. This might be

the reason why we have a different critical resistance.

57

Figure 4.10: Logarithm of the sheet resistance vs. temperature for a 7 UC thickYBCO film at different VG in 9 T magnetic field. From bottom to top: VG =0,0.1, 0.3, 0.5, 0.7, 0.8, 0.9, 1.0, 1.1, 1.12, 1.14, 1.17, 1.20, 1.25, 1.30, 1.35, 1.40,1.44, 1.48 , 1.52 (V).

58

Figure 4.11: Isotherms of R(x) at temperature ranging from 2 K to 22 K derivedfrom Figure 4.10. The carrier concentration x is calculated using the normalresistance at zero magnetic field, i.e., the same as the number used in Figure 4.9.The arrow indicates the crossing point where RC =4.5 kΩ and xc=0.048±0.0005carriers/Cu. Inset: Finite size scaling analysis of R (T ) for data in the range from2 K to 22 K. The best collapse was found when νz = 2.25 ± 0.05.

59

4.3.5 Superconductivity on the electron-doped side

It has been shown that the superconductivity in a ultrathin YBCO film can be

destroyed by a positive gate voltage due to the depletion of holes. In Figure 4.12

we show that by further depletion of holes the superconductivity can be recovered.

This looks more like an electron-doped (n-type) superconductor since depletion of

holes is the same as accumulation of electrons.

Shown in Figure 4.13 and Figure 4.14 are voltage-current(V-I) curves at differ-

ent temperature for two different gate voltages, VG =1.7 and 2.0 V, respectively.

At VG =1.7 V, the evolution of V-I curves shows a typical insulating behavior.

However, at VG =2.0 V, the V-I curve starts to show superconducting behav-

ior at T=80 K. We can define a critical current Ic using a voltage criterion, e.g,

V=0.1 mV. As the temperature decrease from 80 K to 60 K, IC increases. This is

normal since films are usually more superconducting at low temperatures. How-

ever, as the temperature drops below 60 K, the main panel of Figure 4.14 shows

that IC decreases with decreasing temperature. This indicates that there is a

serious localization effect in the electron-doped YBCO and finally at 2 K, the

superconductivity is suppressed. Similar results have been reported by Nojima et

al. [82] but no superconducting behavior can be seen in their sample due to this

localization.

4.3.6 Anomalous behavior on the overdoped side

An underdoped 7 UC thick YBCO film was tuned into the overdoped regime by

means of electrostatic doping using an ionic liquid as a dielectric material. The

gating process was monitored by measuring the sheet resistance as a function of

temperature(Figure 4.15). As can be seen in Figure 4.15(a), the fresh sample,

60

Figure 4.12: R(T) curves at high gate voltage for the 7 UC thick film .

61

Figure 4.13: V-I curves at different temperature for VG =1.7 V. Along the direc-tion of the arrow: T= 200, 160, 120, 80, 60, 40, 30, 25, 20, 18, 16, 14, 12, 10, 8K.

62

Figure 4.14: V-I curves at different temperatures for VG =2.0 V. Main panel:T=60, 40, 35, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12 K. Bottom inset: T=10, 8, 6,4, 2 K.

63

without any applied gate voltage (VG), has a transition temperature TC = 42 K.

Here TC was determined as the temperature corresponding to the crossing of the

extrapolation of the fastest falling part of the R(T) curve to zero resistance. After

the application of a negative gate voltage, TC increased and the normal state

sheet resistance (the metallic region of the curve) droped. This is an indication

that charge carriers are being injected into the sample and the concentration

of holes is increasing towards the optimal doping point. For higher negative gate

voltages, VG = -2.24 to -2.38 V, the rate of change of TC and the normal resistance

slow down and saturate. TC reaches a maximum value of 67 K and the normal

resistance reaches a minimum of 750 Ω at 180 K. Small fluctuations were also

observed in both TC and the normal resistance in this regime. As shown in

Figure 4.15(b), upon a further increase of the negative gate voltage, TC decreased,

suggesting that the sample has been tuned into the overdoped regime. In addition,

the normal resistance increased with increasing negative gate voltage, which is

different from what is found in chemically doped bulk samples [83]. For the highest

negative gate voltages (-2.46 V < VG < -2.56 V) the superconducting transition

is not abrupt and a second transition is turned on at the lowest temperature

part of the R(T) curve. This phenomenon may be associated with the complete

accumulation of holes in the top 1 to 2 unit cells which are the active layers of

the sample, with the insulating dead layer underneath being affected by the high

level of charge transfer.

To check the reversibility of the process and rule out a possible chemical reac-

tion on the sample’s surface the polarity of the gating was reversed. The result is

shown in Figure 4.15(c). After a threshold voltage of about +0.3 V, TC starts to

increase and the normal resistance starts to drop, both of which are evidence of

the recovery of optimal doping. With further increase in the positive gate voltage,

64

shown in Figure 4.15(d), TC drops and the normal resistance increases, revealing

the complete recovery of the initial state of the sample and confirming that the

electrostatic doping process is reversible.

65

Figure 4.15: Temperature dependence of the sheet resistance at different gatevoltages. (a). From 0 to -1.2 V, VG was changed in -0.1 V increments andthen from -1.2 to -2.38 V, the increment was -0.02 V. (b). From -2.38 to -2.56 V,VG was changed in increments of -0.02 V. (c). Negative VG was then removed anda positive VG was added. From 0 to 0.7 V, VG was changed in 0.1 V increments.(d).VG =0.7, 0.75, 0.80, 0.85, 0.90, 0.95, 1.0, 1.05, 1.07, 1.10, 1.13, 1.15, 1.17, 1.20V, then the increment was changed to 0.02 V until VG =1.46V.

66

In order to obtain an independent variable to describe the process of accumu-

lation or depletion of holes an effective hole doping “p” was inferred by using

the generic parabolic relation Tc/Tc,max = 1 − 82.6(p − 0.16)2 [3]. We used this

calculated number of holes to plot TC and the values of normal resistance at 180

K (see Figure 4.16). The open triangles represent the evolution of TC and nor-

mal resistance at 180 K during the accumulation of holes, the depletion process

is represented by the solid triangles. Interestingly, the normal resistance at 180

K exhibits a minimum around the optimal doping point, and its evolution with

the number of holes per CuO2 plane roughly follows the same path in both the

depletion and accumulation processes. This is a surprising behavior since in the

overdoped region of the general bulk phase diagram of cuprates, the normal state

is a Fermi liquid and a lowering of the normal resistance would be expected as

the doping level increased. This raises the possibility that electrostatic doping is

different from the chemical doping of bulk samples. Due to the short Thomas-

Fermi screening length, the electric field affects only the surface layer (1 to 2 unit

cells). Thus we are studying the properties of a 2D system whose physics might

be different from that of bulk samples. Another possible effect, is the strong lo-

calization of the carriers resulting from the high local electric field induced by the

accumulation of anions of the ionic liquid at the surface of the sample, or from

the eventual increase of the electronic disorder at high levels of doping.

Upon closer inspection of Figure 4.16, we noticed that two different regions

can be identified during the gating processes. The first one (region 1) shows an

unchanged TC over a large range of normal resistance change (i.e. gate voltages)

and it plays a primary role at the beginning and the end of the charging processes

as holes are accumulated and depleted, respectively. The second region (region

67

Figure 4.16: Transition temperature (TC ) and normal resistance at T=180Kvs. effective hole doping, p. For both TC and the normal resistance, data withnegative values VG are denoted by open triangles and data with positive VG , bysolid triangles.

68

2) is described above and it shows that the superconducting TC and the nor-

mal resistance at 180 K are correlated and the superconducting properties of the

sample are directly affected by the changes of the gate voltage. This is evidence

that a threshold gate voltage is required for the doping of the superconducting

planes. For gate voltages lower than the threshold, TC is not affected and the

doping process is manifested only by the changes of the normal resistance (region

1). Once the threshold is reached the superconducting properties are affected

correspondingly (region 2).

Since the normal resistance is determined by the carriers both on the CuO2

planes and on the CuOx chains while the superconducting property is mainly

determined by the carriers on the CuO2 planes [73], our data suggest that the

electrostatic doping of YBCO is actually a two-step process. First carriers are

induced on the CuOx chains and second, once a threshold concentration is reached,

charge transfer occurs from the CuOx chains to the CuO2 planes. In a previous

study on NdBa2Cu3O7 in a backside gate configuration [66], Salluzzo et al. found

that the holes injected by the electric field mainly dope the CuOx chains while the

CuO2 planes are only affected by the intra unit cell charge transfer from the CuOx

chains. Here we see that this charge transfer can happen only after a threshold

carrier concentration on the CuOx chains is reached and before this threshold, the

electrostatic doping can affect only the CuOx chains while the CuO2 planes are

kept almost untouched. This two-step electrostatic doping process appears to be

different from that of chemical doping, in which any changes of the hole doping in

the range of 0.05<p<0.2 will affect the normal resistance and the superconducting

properties simultaneously .

To develop insight into the nature of the anomalous normal resistance behavior

in the overdoped region, we measured the Hall resistance at 180 K at different gate

69

Figure 4.17: (a) and (b), Hall resistance (Rxy) vs. magnetic field at T=180K fordifferent gate voltages. From 0 to -2.32 V, VG changes -0.04 V every time andfrom -2.32 to -2.52 V VG changes -0.02 V every time. (c), Normalized Hall number(nH) vs. hole doping p.

70

voltages. Figures 4.17(a) and 4.17(b) show the linear dependence of the transverse

Hall resistance on magnetic field for different gate voltages. Hall resistances show

a positive slope, which indicates that the charge carriers are holes as expected.

In Figure 4.17(c) the normalized Hall number as a function of hole concentration

is shown. The Hall number is calculated from nH = 1/(RHe), being RH the Hall

coefficient which is determined from the slope of the linear fit of the data plotted

in Figs. 4.17(a) and 4.17(b). Interestingly, we find that the Hall number increases

with the hole concentration up to p∼0.15 whereupon an abrupt change takes place

and a peak is developed.

The Hall effect of high-TC cuprates has been long studied and two scenarios

have been proposed. One is the two relaxation time model [84, 85], in which the

Hall relaxation rate 1/τH and the transport scattering rate 1/τtr are associate

with spins and charges respectively. In the other scenario one has to consider

the scattering from different regions of the Fermi surface [86]. Experimentally,

anomalous dependence of the normal state Hall coefficient on the doping level has

been reported in chemically doped YBCO [87], Bi2Sr1.51La0.49CuO6+δ (BSLCO)

[88] and LSCO [89]. In YBCO the Hall conductivity at 125 K showed anomalous

behavior around the 60-K phase and in BSLCO and LSCO, nH peaks around the

optimal doping level at low temperature when superconductivity is suppressed

by ultra high magnetic field. These anomalous behaviors are closely related to

an unusual electronic state or a sudden change in the Fermi surface, although

chemical doping might also change the magnetic coupling thus change the Hall

scattering rate.

For electrostatic doping, it is hard to imagine that an electric field will change

the magnetic coupling. Thus the nH peak we observed indicates that there might

71

be an electronic phase transition in the Fermi surface. Interestingly, in our re-

sults, the peak of the Hall number is found to be at p∼0.15, to the left of the

optimal doping point (p=0.16). For a doping level of p=0.15 the value expected

for T∗, the pseudogap crossover temperature, roughly matches 180 K [90]. This

would indicate that the electronic phase transition occurs at the boundary of the

pseudogap state and the strange-metal state in the bulk phase diagram. How-

ever, the parabolic relation we used to derive the effective doping level might not

be quantitatively right for a 2D film. Thus it is only safe to say the electronic

phase transition we observed is around the optimal doping level, separating the

underdoped regime and the overdoped regime.

Quantum oscillation experiments [73, 91, 92, 93] showed that while there is a

large hole-like Fermi surface in the overdoped regime, there are only small pock-

ets in the underdoped regime. Angle Resolved Photoemission Spectroscopy also

showed that the transition from the overdoped to the underdoped regime is ac-

companied by an electronic reconstruction of the Fermi surface [94, 95, 96, 97, 98].

Thus an electronic phase transition in the Fermi surface is expected around the

optimal doping regime. However, this anomalous behavior has never been widely

reported in bulk samples and the similar peak observed in Ref. [88] disappeared

at high temperature. This suggest that the electronic phase transition has been

enhanced in our film, either due to the low dimensionality or the high local electric

field.

Chapter 5

Conclusions and Future

Directions

5.1 Conclusions

The electrical transport properties of ultrathin YBa2Cu3O7−x films were measured

to study the superconductor-insulator transition induced by electrostatic charging.

Backside gating using SrTiO3 as a dielectric insulator showed only small TC shifts,

which confirmed the special electrostatic doping mechanism of YBCO. In fact, the

carriers are mainly induced on the CuOx chains while the CuO2 planes are only

indirectly affected. As a consequence, a much larger carrier transfer is required to

study the SI transition in YBCO.

Top gating using an ionic liquid as a dielectric makes it possible to tune the

SI transition in YBCO due to the “magic” properties of ionic liquids. Transport

measurements on a 7 unit cell thick film show a clear evolution from superconduc-

tor to insulator. A phase diagram has been derived from the R(T) curves and it

is similar to the bulk phase diagram. This is surprising considering the fact that

72

73

the active layer is only one to two unit cells thick, and that there are high local

electric fields at the interface. A finite size scaling analysis showed that the critical

resistance (6.0 kΩ) is close to the quantum critical resistance (6.45 kΩ) and all

resistance data collapsed onto a single scaling function with a critical exponent

νz = 2.2 except the lowest temperature. The critical exponent product is con-

sistent with the one associated with quantum percolation theory. However, new

physics appears to develop at the lowest temperatures, resulting in an indirect SI

transition.

In the presence of a magnetic field, a much cleaner SI transition was revealed

in the electrostatic charging of the same 7 unit cell thick film. This suggests the

indirect SI transition in zero field might come from superconducting islands or a

superconducting underlayer, which is suppressed by magnetic field. A finite size

scaling analysis shows that this SI transition is still a quantum phase transition

and the universality class does not change in the presence of magnetic field. The

critical carrier concentration shifts to a higher level. The data also show that the

critical resistance is not universal.

Further depletion of holes is the same as accumulating electrons and an electron-

doped superconductor was revealed in the same YBCO film. The I-V curves ver-

ified the evolution from insulator to superconductor on the electron doped side.

However, the carrier of the electron doped superconductor are localized and the

superconductivity is suppressed at the lowest temperature.

In addition, by the accumulation of holes, an underdoped YBCO film was suc-

cessfully tuned into the overdoped regime. This process proved to be reversible. A

two-step doping mechanism for electrostatic doping of YBCO was revealed. Trans-

port measurements showed a series of anomalous features compared to chemically

doped bulk samples. The normal resistance increased with carrier concentration

74

on the overdoped side and the high temperature (180 K) Hall number peaked at

a doping level of p∼0.15. These anomalous behaviors suggest that there is an

electronic phase transition in the Fermi surface around the optimal doping level.

5.2 Future directions

While our results have successfully revealed the superconductor-insulator transi-

tion in YBCO and extended our knowledge to the overdoped and electron doped

side, there are many improvements and other experiments that could be done.

First, PBCO buffer layers can be used to improve the quality of the YBCO

films and would allow the experiments to be carried out in a more controllable

way. In our experiments, the active layers are estimated to be 1-2 unit cells.

However, the YBCO underlayers might also be affected by electrostatic charging

and lead to inhomogeneities, especially when the gate voltage is very high. This

problem can be eliminated by using a PBCO buffer layer.

Second, more transport measurements can be done in the SI transition regime

and on the highly underdoped samples. Near the transition point, a relative small

magnetic field might induce a SI transition. As for the highly overdoped side,

there might be another SI transition at the point where the superconductivity

disappears. Studies of the properties of these SI transitions will contribute to the

understanding of high-temperature superconductivity.

Third, the electronic and magnetic state in the SI transition regime needs

to be studied to promote a further understanding of the fundamental physics.

Since we are studying ultrathin films, a lot of techniques used to study single

crystals, such as ARPES and neutron scattering, are not applicable. Electron

spectroscopy and muon-spin rotation might be possible but there are still a lot of

75

technical challenges. For example, there is an ionic liquid on top of the film and

the field effect is confined to the first 1-2 unit cells.

There are a lot of other experiments in which the structure and symmetry

could be measured once those difficulties have been overcome.

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Appendix A

Acronyms

Table A.1: Acronyms

Acronym Meaning

AF antiferromagnetic

ARPES angle-resolved photoemission spectroscopy

FET field-effect-transistor

IC critical current

MBE molecular beam epitaxy

nH Hall number

PBCO PrBa2Cu3O7−x

RS sheet resistance

R (T ) resistance vs. temperature

SI superconductor to insulator

STO SrTiO3

Continued on next page

90

91

Table A.1 – continued from previous page

Acronym Meaning

Tc critical temperature or transition temperature

UC unit cell

V-I voltage-current

VG gate voltage

YBCO YBa2Cu3O7−x