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Odd frequency pairing in superconducting heterostructures. Alexander Golubov Twente University, The Netherlands. Y. Tanaka Nagoya University, Japan Y. Asano Hokkaido University, Japan Y. Tanuma Akita University, Japan. Contents. (1) What is odd-frequency pairing - PowerPoint PPT Presentation
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Y. TanakaNagoya University, Japan
Y. AsanoHokkaido University, Japan
Y. TanumaAkita University, Japan
Alexander GolubovTwente University, The Netherlands
Odd frequency pairing in
superconducting heterostructures
Contents
(1) What is odd-frequency pairing
(2) Normal metal / Superconductor junctions
(3) Ferromagnet/Superconductor junctions
Conventional Classification of Symmetry of Cooper pair
Spin-singlet Cooper pair
s-waved-wave
Spin-triplet Cooper pair
Even Parity
Odd Parity
p-wave
BCSCuprate
3He Sr2RuO4
Pair amplitude(pair correlation)
Exchange of two electrons
Fermi-Dirac statistics
Pair amplitude
Exchange of time
Even-frequency pairing (conventional pairing)
Odd-frequency pairing
Odd-frequency pairing
Pauli principle
Symmetry of pair wave functions:
spin-singlet: = odd
spin-triplet: = even
even-frequency superconductivity
odd-frequency superconductivity
()
(ω), f(ω)
(ω), f(ω)
s-, d-wave
s-, d-wave
p-, f-wave
p-, f-wave
Symmetry of the pair amplitude
Frequency( time) Spin
+(even)
odd)
+(even)
odd)
+(even)
Orbital
+ symmetric, anti-symmetric
ESE
ETO
OTE
OSO
singlet)
Total
(odd)+ (triplet)
+ triplet)
ESE (Even-frequency spin-singlet even-parity) ETO (Even-frequency spin-triplet odd-parity)OTE (Odd-frequency spin-triplet even-parity) Berezinskii
OSO (Odd-frequency spin-singlet odd-parity) Balatsky, Abrahams
singlet)
+(even)
(odd)
BCS
Cuprate
3HeSr2RuO4
Previous studies about odd-frequency pairing
Bulk state (Pair potential, Gap function) Berezinskii (1974)Balatsky Abrahams Schrieffer Scalapino(1992-1993)Zachar Kievelson Emery (1996)Coleman Mirranda Tsvelik (1997)Vojta Dagotto (1999)Fuseya Kohno Miyake (2003)
Junction (No pair potential)Induced odd-frequency pair amplitude in ferromagnet attached to spin-singlet s-wave superconductor Bergeret, Efetov, Volkov, (2001)
Odd-frequency pairing state
• Odd-frequency pairing state is possible even if we start from the conventional even-frequency paring state:
Broken spin rotation symmetry or spatial invariance symmetry can induce odd-frequency pairing state:
- ferromagnet/superconducor junctions
- non-uniform systems
Contents
(1) What is odd-frequency pairing
(2) Ballistic normal metal junctions
( 3 ) Diffusive normal metal junctions
(4 ) Ferromagnet/Superconductor junctions
Ballistic junction
Y. Tanaka, A. Golubov, S. Kashiwaya, and M. Ueda Phys. Rev. Lett. 99 037005 (2007)
M. Eschrig, T. Lofwander, Th. Champel, J.C. Cuevas and G. SchonJ. Low Temp. Phys 147 457(2007)
BallisticNormal metal(semi-infinite)
Superconductor(semi-infinite)
Eilenberger equation
ballistic normal metal
S
Form factor
SN
x0
(explicitly denote direction of motion)
Bulk state
Quasiparticle function
Pair amplitudes
Only
Pair potential
General properties ( frequency)
Odd-frequency(imaginary) Interface-inducedcomponent
Even-frequency(real)bulk-component
Spatial change of the pair potential
Superconductor is conventional even-frequency one.
Normal metal spin-triplet p-wave superconductor
px-wave component of ETO pair amplitude
s-wave component of OTE pair amplitude
(high-transparent)
(low-transparent)
Y. Tanaka, et al PRL 99 037005 (2007)
ETO (Even-frequency spin-triplet odd-parity)OTE (Odd-frequency spin-triplet even-parity)
Pair potential
Symmetry of the bulk pair potential is ETO
Underlying physics
Near the interface, even and odd-parity pairing states (pair amplitude) can mix due to the breakdown of the translational symmetry.
The interface-induced state (pair amplitude) should be odd in frequency where the bulk pair potential has an even -frequency component since there is no spin flip at the interface.
Fermi-Dirac statistics
Mid gap Andreev resonant (bound) state
(MARS)
Interface (surface)
+ー
–1 0 10
2
4
Nor
mal
ized
DO
S
Local density of state has a zero energy peak. (Sign change of the pair potential at the interface)
Tanaka Kashiwaya PRL 74 3451 (1995), Rep. Prog. Phys. 63 1641 (2000) Buchholz(1981) Hara Nagai(1986)Hu(1994) Matsumoto Shiba(1995)Ohashi Takada(1995)Hatsugai and Ryu (2002)
+ー
ー+
Mid gap Andreev resonant (bound) state
Electron-like quasiparticle
Hole-like quasiparticle
Cooper pair
Odd-frequency Cooper pair( Odd-frequency pair amplitude )
Y. Tanaka, Y. Tanuma and A.A.Golubov, Phys. Rev. B 76, 054522 (2007)
Odd-frequency pairing state in N/S junctions (N finite length)
Bounds state are formed in the normal metal
Ratio of the pair amplitude in the Nregion (odd/even)
At some energy, odd-frequency component can exceed over even frequency one.
Odd-frequency pairing
Even-frequency pairing
Hidden odd-frequency component in the s-wave superconductor junctions
Ratio of the pair amplitude at the N/S interface and the bound state level
Bound states condition (Z=0)( McMillan Thomas Rowell)
Bound states are due to the generation of the odd-frequency Cooper pair amplitude
Odd-frequency pairing
Even-frequency pairing
Y. Tanaka, Y. Tanuma and A.A. Golubov, PRB 76 054522 (2007)
(1)
(2)
(3)
(4)
• ESE (Even-frequency spin-singlet even-parity)• ETO (Even-frequency spin-triplet odd-parity)• OTE (Odd-frequency spin-triplet even-parity)• OSO (Odd-frequency spin-singlet odd-parity)
Bulk state
ESE (s,dx2-y2 -wave)
ESE (dxy-wave)
ETO (px-wave)
ETO (py-wave)
Sign change(MARS)
No
Yes
Interface-induced symmetry(subdominant component )
Yes
No
ESE + (OSO)
OSO +(ESE)
OTE + (ETO)
ETO + (OTE)
Symmetry of the Cooper pair (No spin flip)
Phys. Rev. Lett. 99 037005 (2007)
(1) (2) (3) (4)
Contents
(1) What is odd-frequency pairing
(2) Ballistic normal metal junctions
( 3 ) Diffusive normal metal junctions
(4 ) Ferromagnet/Superconductor junctions
Impurity scattering effectTanaka and Golubov, PRL. 98, 037003 (2007)
BallisticNormal metal
Superconductor
DiffusiveNormal metal
(DN)Superconductor
Impurity scattering (isotropic)Only s-wave pair amplitude exists in DN
(1)ESE (2)OTE
ESE (Even-frequency spin-singlet even-parity)OSO (Odd-frequency spin-singlet odd-parity)
Usadel equationAvailable for diffusive limit
Angular average
Diffusivelimit
Diffusive normal metal region attached to superconductor
DN S
Even frequency spin singlet even parity (ESE) pair potential
Even frequency spin singlet s-wave (ESE) pair is induced in DN.
ESE pair /ESE pair potential
DN S
Even frequency spin singlet even parity (ESE) pair potential
s-wave case
–0.3 0 0.30
1
Even frequency spin singelt s –wave
s–wave
DN
+ー
Px-wave case
New type of proximity effect
Odd frequency spin triplet s-wave (OTE) pair is induced in DN
Y.Tanaka, A.A.Golubov, Phys.Rev.Lett. 98, 037003 (2007)
)(Re f)(Im f
DN
+ー
Even frequency spin triplet odd parity (ETO) pair potential
–0.3 0 0.30
1
2
Even frequency spin triplet p–wave
px
py
DN
+
ー
(no proximity& no MARS)
Px-wave case
Py-wave case
Symmetry of the pair potential Induced pair amplitude in DN
Even frequency spin singleteven parity (ESE)
Even frequency spin tripletodd parity (ETO)
Odd frequency spin tripleteven parity (OTE)
Odd frequency spin singletodd parity (OSO)
ESE
OTE
OTE
ESE
Summary of Proximity effect (diffusive normal metal)
How to detect triplet superconductor
MARS (Mid gap Andreev resonance state) can penetrate into DN by proximity effect only for triplet superconductor junctions
LDOS in DN has a zero energy peak
Diffusive normal Metal (DN)
STS
Triplet superconductor
MARS
Diffusive normal Metal (DN)
STS
Singlet superconductor
MARS
LDOS in DN does not have a zero energy peak
ZEP No ZEP
How to detect odd-frequency paring amplitude: measuring electrical conductivity Asano, Tanaka, Golubov, Kashiwaya, PRL 99, 067005 (2007)
Sr2RuO4
Au :I+
Au :V+
Au :I-
Au :V-Kashiwaya, Maeno 2007
Zero energy peak No Zero energy peak
OTE proximityESE proximity (conventional)
OTE (Odd-frequency spin-triplet even-parity)
ESE (Even-frequency spin-singlet even-parity)
Contents
(1) What is odd-frequency pairing
(2) Ballistic normal metal junctions
( 3 ) Diffusive normal metal junctions
( 4 ) Ferromagnet/Superconductor junctions
_
Odd frequency spin-triplet s-wave pair
SuperconductorFerromagnet
Bergeret, Efetov, Volkov, (2001)Eschrig, Buzdin, Kadigrobov,Fominov, Radovic
Generation of the odd-frequency pair amplitude in ferromagnet
Odd-frequency pair amplitude (not pair potential) is generated in ferromagnet
junctions
spin-singlet s-wave pair+
F FSd f d f2d s
x x
z z
triplet Josephson effect in SF multilayered system with noncollinear ferromagnets and thin superconductors
(x) /
x
FS
D
h
D<<
s in g le t: tr ip le t:
Spin triplet Cooper pairs in SF systems
Josephson current in S/HM/S
Half metal : CrO2Keizer et.al., Nature (2006)
Eschrig et. al., PRL(‘03)Theory in the clean limit
Spin active interfaceBergeret et. al., PRL(‘01),
Kadigrobov et. al., Europhys Lett.(‘01)
Lofwander and Eschrig, Nature Physics (2008)
Furusaki, Physica B(‘92), Asano, PRB(‘01)
Advantages
SNS, SFS, S/HM/S
22
1
JJJ
JJSN
ii
Parameters
S
ex
V
V : exchange: spin-flip
Recursive GF
Y.Asano, Y. Tanaka, A.A.Golubov, Phys.Rev.Lett. 98, 107002 (2007)
Spin active interface2SVσV
JJ
self-averaging
SFS, S/HM/S
30 ,, ffff
ff
No sign change
SFS
3,, fff
0f
fS/HM/S
only
odd-frequency pairs
-1.0 -0.5 0.0 0.5 1.0
-0.5
0.0
0.5
1.0
< f >
Pair
ing
func
tion
/ fB
< f0 >
n /
0
Odd-frequency pairs
SFS
3,, fff
0f
f
S/HM/S
only
even-odd mix pure odd
Quasiparticle DOS in Half Metal
0.0 0.5 1.00
1
2
3
LD
OS
at j
= 37
/ n
0
S/HM/S
SNS
E /
Zero Energy Peak
can be detectedby tunneling spectroscopy
Conclusions(1) Ubiquitous presence of the odd-frequency pair PRL 99, 037005 (2007)
(2) Odd-frequency pair amplitude is enhanced in the presence of the midgap Andreev resonant state (PRL 99, 037005 (2007)).
(3) Low energy Andreev bound states can be expressed in terms of odd-frequency pairing (PRB 76 054522 (2007))
(4) The origin of the anomalous proximity effect in DN/spin-triplet p-wave junction is the generation of the odd-frequency pairing state.
(PRB 70, 012507 (2004), PRL 98 037003 (2007) , PRL 99 067005 (2007))
(4) Odd-frequency pairs carry supercurrent in S/HM/S junctions (PRL 98, 107002 (2007))