andreev bound states in anisotropic superconductor junctions · 2009. 10. 2. · scope of this...
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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