Andreev bound states in anisotropic superconductor junctions

S. Kashiwaya AIST

Y. Tanaka Nagoya University

AIST H. Kambara, H. Kashiwaya, T. Matsumoto

Tokyo Univ of Sci. T. Furuta, H. YaguchiHokkaido Univ. Y. AsanoKyoto Univ. Y. Maeno

Collaborators

1 Scope of this conference2 Experiments on Sr2RuO4

Scope of this conference

Phenomena Physics Materials

Andreev Reflection&

Coherence of QP'sChiral p-wave

superconductorsOdd frequency pairing

A11,A12A4,A5,A6, B1, B3, B4, B5, B6 A1,A2,A3

Ferromagnetic&

spin related effectsTopological superconductor Iron pnictide

B8,B9,B10 B11,B12,B13A7,A8,A9,A10, B2

Vortex physics

A13,B7,B14

New direction of superconducting nanostructure

Normal metal Superconductor

electron

hole

Cooper pair

Fermi energyEnergy gap ∆

electron

Andreev reflection

An elemental scattering process at S/N interface

When an electron injection from N side (E<∆) Two possible reflection processes

Normal reflection : injected electron reflected as electron

Andreev reflection : injected electron reflected as hole

Andreev reflection1 The injected electron finds another electron to form a Cooper pair

and goes into superconductor

2 The left hole is retro-reflected as Andreev reflection

( )221 baevF −+∝σ

BTK formula (Blonder et al, 1982)

2a Amplitude of Andreev reflection2b Amplitude of normal reflection

Conductance of this junction is described by

Andreev bound statesThe spatial variation of pair potential yields quasi-particle bound states in superconductors.

Normal metal

electron

hole

Superconductor

Cooper pair

Superconductor

Cooper pair

φ1 φ2

1 The electron (E<∆) in the normal metal cannot enter into both sides of superconductors as the quasiparticle

2 They form discrete bound states by repeating the multiple Andreev reflectionat S/N boundaries

1 2 3 4 5 6

-1

-0.5

0.5

1

Zero-energy bound states at the phase difference of π

Energy level of bound states as the function of phase difference

−+ −φφphase difference

Long standing issues: ABS related phenomena

DC Josephson Current: ABS carries Josephson current

lelectron

hole

Cooper pairCooper pair

Zn impurity in Bi2212Pan, 2001ABS around impurity

All these phenomena have the same origin!

Andreev reflection and ABS

SN

SNS junction

Vortex core statesH. F. Hess, 1990

Ishii, 1979

DeGennes-Saint James bound states

ABS in normal metal side of Clean normal metal/s-wave

Surface Andreev bound states in anisotropic superconductorsIn the case of anisotropic superconductors, pair potentials of different phases and amplitudes are interfolded in momentum space.

∆+

∆-

Surface scattering

Hu, 1994, Tanaka, Kashiwaya, 1995

Pair potential

depth

∆

Localized zero-energy ABS

dxy-wave pair potential

Ru-Oxide

SrRuO4 (Mao, Yaguchi)

Organic

κ-(BEDT-TTF)2Cu[N(CN)2]Br

(Ichimura)

Heavy Fermion

UBe13 (Ott)

CeCoIn5 (Wei)

Bound states are formed at the surface

Scope of this conference

Phenomena Physics Materials

Andreev Reflection&

Coherence of QP'sChiral p-wave

superconductorsOdd frequency pairing

A11,A12A4,A5,A6, B1, B3, B4, B5, B6 A1,A2,A3

Ferromagnetic&

spin related effectsTopological superconductor Iron pnictide

B8,B9,B10 B11,B12,B13A7,A8,A9,A10, B2

Vortex physics

A13,B7,B14

New direction of superconducting nanostructure

General description of Cooper pairIn recent theoretical works, the physical origin of ABS is becoming more clearer.

Pair amplitude )',(),(ˆˆ),( '' sskcckF skskss χωωrr

rr Φ=⟩⟨=−

orbital

spin

frequencyPair amplitude Fss’(k) must be an odd function with respect to the permutation of electrons.

Conventional consensus of Cooper pairsEven for ω

Even Frequency pair potential

odd-even singlet s-wave , singlet d-wave even-odd triplet p-wave , triplet f-wave

Spin Orbital

Gapped states

Recent improvement clarified

odd-odd singlet p-wave, singlet f-waveeven-even triplet s-wave, triplet d-wave

Spin OrbitalOdd for ω

Odd Frequency pair potential

Ungapped statesBerezinskii, Balatsky-Abrahams, Abrahams-Balatsky-Schrieffer-Allen, Vojta-Dagotto

Possible symmetry conversion in proximity effect

Odd frequency pairs are easily produced from even frequency pairsthrough symmetry breaking.

Real space: Edge, non-magnetic impurity, non-uniformity Tanaka, 2006

triplet ⊗ p-wave ⊗ even-freq triplet ⊗ s-wave ⊗ odd-freq

Momentum related conversioneven odd even even

Spin space: Spin active interface, spin flip scattering Bergeret, Volkov, Efetov, 2001

Spin related conversionsinglet ⊗ s-wave ⊗ even-freq triplet ⊗ s-wave ⊗ odd-freqodd even even even

Ubiquitous presence of odd-frequency pairing statesOdd frequency component is ubiquitously exist in non-uniform superconductors.

The ratio of pair potential amplitude of even and odd

S-wave

Clean normal metalOdd-frequency pairing

Even-frequency pairing

Y. Tanaka, Y. Tanuma A.A. Golubov, PRB 76 054522 (2007)

Coincide with DeGennes-Saint James bound states

DeGennes-Saint James bound states are composed of odd frequency pairing states.Odd frequency pairs were treated unconsciously in old problems.

Reinterpretation of zero-energy ABSTanaka,2007Back to the surface ABS case

Even frequencyEven parity

Odd frequencyOdd parity

x0

Even frequency component Gapped states

Odd frequency component Ungapped states

ZBCP at dxy-surface is reinterpreted as odd frequency pairing componentinduced by the scattering at the interface.

Close correlation between ABS and odd frequency pairing is becoming clearer.

Experimental results: anomalous Josephson current in CrO2

Josephson current through half metallic ferromagnet CrO2

Bergeret, Volkov, Efetov, 2001Asano

↑↓−↓↑

even freq.s-wave

↑↓−↓↑

even freq.s-wave

↑↑

odd freq.s-wave

Nb

CrO2

spin active interface

Possible explanation

R. S. Keizer, et al, 2006

We expect a lot of novel phenomena will be discovered through odd frequency research.

How to detect odd frequency proximity effect more clearly?

1 Spectroscopy of DN/Px

2 Josephson effect of Px/DN/Px

3 Transport experiments

px DN

–0.1 0 0.1 0.20

2

4p–wave

LDO

S(N

orm

aliz

ed)

px DN px

Asano, 2007

Odd freq. component has zero-energy peak in DOS

Anomalous temp. dep. due to odd

STMtip

P-wave superconductor is suitable for these purposes.We expect p-wave micro-devices will be studied more in detail.

Feature of the Andreev bound states for various types of superconductors

Surface ABS at the edge of anisotropic superconductors is discussed in the relation of topology.

Non-centrosymmetricsuperconductors

(Helical)

dxy,wave Chiral p-wave

Spin currentNo net edge current

k

Chiral gapless edge statesSpontaneous current at edge

k k

Integer quantum Hall system Quantum spin Hall systemAnalogy

These three types have different surface ABS topology.Topology related new physics coming out from the topology of gap function.

New materials and functionality

1 Iron Penictide

2 New functionalitySuperconductor-based LE : π junction in SFS for Qubit

Tc～55K

Pairing mechanism?

Hosono group 2008

S /F/ SSuemune, Takayanagi

Scope of this conference

Phenomena Physics Materials

Andreev Reflection&

Coherence of QP'sChiral p-wave

superconductorsOdd frequency pairing

A11,A12A4,A5,A6, B1, B3, B4, B5, B6 A1,A2,A3

Ferromagnetic&

spin related effectsTopological superconductor Iron pnictide

B8,B9,B10 B11,B12,B13A7,A8,A9,A10, B2

Vortex physics

A13,B7,B14

We will find “New direction of superconducting nanostructure”through these discussions

Transport properties in microfabricated Sr2RuO4 devicesSuperconducting states of Sr2RuO4Maeno, 1994

d = ∆0z (kx iky): chiral p-wave±Layered perovskite

Equal spin pair d//ZOrbital moment (Lz = 1or-1)

This material best to study 2D chiral p-wave physics!

Quasi-2D Fermi surface

Mesoscopic Sr2RuO4 devices

Sr2RuO4 is unique material with complex order parameter, we expect novel functionalities in ruthanate microdevices .Unfortunately, no thin film of superconducting Sr2RuO4Then we develop novel microfabrication process by using FIB from single crystals.

V+

V-

abcFIB

Sr2RuO4single crystal

I+

I-V-V+

Au

70 µm

We have already fabricated various types of ruthanate based microdevices,

Weak link bridge C-axis junction T-shape junction SQUID

20µI+

V+

I-

V-

5µ

20µ

3.5µ

Advantages of FIB process compared with conventional lithography process

1 Applicable for various superconductors even without thin films2 3-Ddevice fabrication is possible.

Intrinsic junction Bi2212

Bi2Sr2CaCu2O8+δ

lc>ξc

d-wave

Tunneling

Intrinsic junction of Sr2RuO4

Sr2RuO4

lc<ξc

p-wave

-4 -2 0 2 4-200

-100

0

100

200

I (mA)V

(µV

)

T = 1.0 K

Weak link

Details are presentd in H. Kambara, next talk.

Targets of Sr2RuO4 today's presentation

1 Clarify the transport properties of weak link

Critical current in bridges

Novel switching due to chiral domain wall motion

2 Detect of vortex states using SQUID's

Searching for predicted half vortex quantum

Future application :Topological quantum computing

More details H.Kambara, next talk

Typical properties of in-plane Sr2RuO4 bridge

-4 -2 0 2 40

0.5

1

I (mA)

(dV

/dI)

/ (dV

/dI) 4

.2 K

3-K (c199-4) 追加工③ (08/3/3-5)

CAL_080303IV_4.2K_PU.DATCAL_080303IV_1.8K_PU.DATCAL_080303IV_1.7K_PU.DATCAL_080303IV_1.6K_PU.DATCAL_080303IV_1.5K_PU.DATCAL_080305IV_4.2K.DATCAL_080305IV_3.0K_PU.DATCAL_080305IV_2.5K_2.DATCAL_080305IV_2.2K_2.DATCAL_080305IV_2.0K.DAT

4.2 K 3.0 K 2.5 K 2.2 K 2.0 K 1.8 K 1.7 K 1.6 K 1.5 K

dV/dI-I

Ic

FIB image

1 2 3 40

0.5

1

T (K)

R /

R4.

2K

3-K (c199-4)R-T

Magnetic field response of dV/dI

0.4 0.6 0.8 10

2

4

6

T/Tc0

I c0 (m

A)

c199-8FIB② (20*6*6) FIB③ (10*3*6 (center)) Conventional Ic-T

I [mA]

B[gauss]

Ic suppression due to magnetic field

All these features are mostly consistent weak link type Josephson junctions (JJ)Thus we believe weak link JJ's of ruthante are successfully fabricated.

Anomalous feature : bridge size dependence of Ic, Jc

NeckingS

L

W

t: thickness

I // ab S = Wt

SLRbridge ρ=

SJI cc ×=

In conventional case,

Critical current density: Jc

Resistance

Conventional behavior in Nb thin films(Ic ~ Jc S)

S

conventional

In the case of the smallest junction,Jc is two order of magnitude enhanced

as compared to known bulk value.

0

0.05

0.1

0.15

L / R

brid

ge (m

/Ω)

c199-4 c199-20 c199-8 c199-9 c359-2 c359-7

thickness

width

T = 4.2 K

0 1 2[×10-9]

0

1

2

I c0 (n

orm

aliz

ed)

S (m2)

c199-4 c199-20 c199-8 c199-9 c359-2 c359-7

Anomalous Jc enhancement in Sr2RuO4 bridges

Ic tends to be insensitive to S

0 1 2[×103]

102

103

104

J c (A

/cm

2 )

S (µm2)

c199-4 (1.4 K) c199-20 (1.3 K) c199-8 (1.2 K) c199-9 (1.3 K) c359-2 (1.4 K) c359-7 (1.3 K) Unusual

!Jc (0) = 500 A/cm2

for bulk pure Sr2RuO4(by Deguchi and Maeno)

conventional

conventional

Resistance shows conventional dependence No problem in fabrication

What is the origin of Jc enhancement?× Conventional explanation: non-uniformity of Jcdue to Meissner effect

Sample thickness (t) after FIB milling is comparable to λ(0) (penetration depth) though W >> λ.

λ (0) = 0.15 µm (ab), 3.0 µm (c)

Grenko, (2002)Jc enhancement in experiments is far larger than expected

Possible explanation: high current channel formation along edgeSupercurrent only along edge?

High Jc edge channel formation !But the origin this channel is unclear.A links to chiral gapless edge states?

+-

+-+-+-

Ic almost constant against the necking

necking

The influence of edge channel appear as hysteresis in I-V H. Kambara, next talk

Detection of vortex in 2D chiral p-wave superconductorDifferently from conventinal s-wave superconductors, vortex in multi-component superconductors can take fractional form.

( ) )exp()( 0 kyx iikk ))

ϕ±∆= dkd

spin orbital

d-vector

Φ0/2

d-string

l-vector↓↓↑↑= ,, 21 φφyx ikk ,, 21 =φφ

Most plausible pair potential form

l-stringkx+iky

kx-iky

Ichioka, et al. 2004d-vectorVolvik, 1998

Ivanov, 2001

Two types of half quantum vortex in principle.d-type l-type

Φ0/2

Φ0/2

Φ0/2

Maeno, 2003

Stability of HQV's （∆E=Ehalfpair-Efull）

d-type: S. B. Chung et al. (2007)

Stability in superconducting thin slabs ∆E as the function of superconductor size

The stability is determined by the competition:Energy gain: vorticity(magnetic potential)Energy loss: string potential

HQV's are stabilized in slabs when the size of the slab is 2-3 times of penetration depth.

l-type: Ichioka, et al. (2004)

l-type HQVs are stabilized at the chiral domain walls.

How to detect HQV's in Sr2RuO4.Magnetic field modulation of SQUID

Φ0 / 2

∆↑↑ ∆↓↓

Φ0

B= n Φ0/2

Φ0 / 2

shielding current

B= n Φ0

0

Ｉｃ

conventional

0 1

Periodicity is Φ0/SConventional s-wave DC-SQUID

-1 1 Φ/ Φ0

Chiral p-wave DC-SQUID with stable HFQ

0

0 1/2 1

Periodicity is Φ0/2S?

-1 1 Φ/ Φ0

Fabrication of Sr2RuO4 SQUID and temperature dependence and dV/dI

FIB images

Expected Ic modulation cycle (Φ0) is 0.7 gauss

0 20 40 60 80 1000

0.02

0.04

0.06

T (K)

R (Ω

)

3-K (c199-20) 追加工⑥-3 (09/8/13)

Imod= 87 µA

cooling warming

-5 0 50

0.2

0.4

0.6

I (mA)

(dV

/dI)

/ (dV

/dI) 4

.2 K

, 0 m

A

3-K (c199-20) 追加工⑥-3 (09/8/13)

→ ← →

1.0 K-2 0.8 K-1

1.3 K-7 1.3 K-3

1.3 K-8 1.3 K-6 1.3 K-5

1.3 K-4

Ic

dV/dI-I

R-T

Magnetic field response of Sr2RuO4 SQUID

Mapping of dV/dI Mapping of dV/dI

0-3G1.3K

Ic

B[gauss]

Ic

B[gauss]

Flux trap?

50-53G1.1K

I [mA]I [mA]

Weak modulation of Ic but not periodic Ic jump possibly due to flux trap No periodic modulation of Ic

Speculation: The presence of the high current edge states disturbs to observe the magnetic field response.We are wondering how we can detect the HQV's.

Summary

1 We develop a fabrication technique for µm-size Sr2RuO4devices using FIB process.

2 We found the high current density edge modein Sr2RuO4 bridges.

It is unclear whether this is peculiar to chiral p-wave superconductors.

3 Magnetic field responses of Ic in Sr2RuO4 SQUID didn't show Ic modulation to the applied field.

Not succeeded in detecting HVQ's.

More details of SRO bridges will be presented by H.Kambara, next talk