1 / 41

Y. Tanaka Nagoya University, Japan Y. Asano Hokkaido University, Japan Y. Tanuma

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

cardea
Download Presentation

Y. Tanaka Nagoya University, Japan Y. Asano Hokkaido University, Japan Y. Tanuma

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Oddfrequencypairingin superconductingheterostructures Alexander Golubov Twente University, The Netherlands Y. Tanaka Nagoya University, Japan Y. Asano Hokkaido University, Japan Y. Tanuma Akita University, Japan

  2. Contents （１）What is odd-frequency pairing （２）Normal metal / Superconductor junctions （３）Ferromagnet/Superconductor junctions

  3. Conventional Classification of Symmetry of Cooper pair Spin-singlet Cooper pair Even Parity d-wave Cuprate s-wave BCS Spin-triplet Cooper pair Odd Parity 3He Sr2RuO4 p-wave

  4. Pair amplitude(pair correlation) Exchange of two electrons Fermi-Dirac statistics

  5. Pair amplitude Exchange of time Even-frequency pairing (conventional pairing) Odd-frequency pairing

  6. Odd-frequency pairing even-frequency superconductivity D(w) Pauli principle D(ω), f(ω) Symmetry ofpairwave functions: w spin-singlet: s = odd odd-frequency superconductivity D(ω), f(ω) s-, d-wave p-, f-wave spin-triplet: s = even w p-, f-wave s-, d-wave

  7. Symmetry of the pair amplitude + symmetric, - anti-symmetric Frequency （time) Spin Orbital Total BCS - (singlet) - +(even) +(even) ESE Cuprate +(even) 3He -(odd) - + (triplet) ETO Sr2RuO4 -(odd) +(even) - + (triplet) OTE -(odd) - - (singlet) -(odd) OSO ESE (Even-frequencyspin-singleteven-parity) ETO (Even-frequencyspin-tripletodd-parity) OTE (Odd-frequencyspin-tripleteven-parity) Berezinskii OSO (Odd-frequencyspin-singletodd-parity) Balatsky, Abrahams

  8. 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)

  9. 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

  10. Contents （１）What is odd-frequency pairing (2) Ballistic normal metal junctions （3）Diffusive normal metal junctions (4）Ferromagnet/Superconductor junctions

  11. Ballistic junction Ballistic Normal metal (semi-infinite) Superconductor (semi-infinite) 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. Schon J. Low Temp. Phys 147 457(2007)

  12. S ballistic normal metal Eilenberger equation (explicitly denote direction of motion) Pair potential Quasiparticle function Form factor Pair amplitudes Bulk state Only S N

  13. Odd-frequency (imaginary) Interface-induced component General properties（frequency) Superconductor is conventional even-frequency one. Even-frequency (real) bulk-component Spatial change of the pair potential

  14. spin-triplet p-wave superconductor Normal metal

  15. Symmetry of the bulk pair potential is ETO (low-transparent) Pair potential (high-transparent) px-wave component of ETO pair amplitude s-wave component of OTE pair amplitude ETO (Even-frequencyspin-tripletodd-parity) OTE (Odd-frequencyspin-triplet even-parity) Y. Tanaka, et al PRL 99 037005 (2007)

  16. Underlying physics Near the interface, even and odd-parity pairing states (pair amplitude) can mix due to the breakdown of the translational symmetry. Fermi-Dirac statistics The interface-induced state (pair amplitude) should beodd in frequency where the bulk pair potential has an even -frequency component since there is no spin flip at the interface.

  17. ー ＋ Mid gap Andreev resonant (bound) state (MARS) 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 ＋ Interface (surface)

  18. Mid gap Andreev resonant (bound) state Electron-like quasiparticle Cooper pair Hole-like quasiparticle Odd-frequency Cooper pair （Odd-frequency pair amplitude）

  19. Odd-frequency pairing state in N/S junctions (N finite length) Bounds state are formed in the normal metal Y. Tanaka, Y. Tanuma and A.A.Golubov, Phys. Rev. B 76, 054522 (2007)

  20. 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

  21. Odd-frequency pairing Even-frequency pairing 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 Y. Tanaka, Y. Tanuma and A.A. Golubov, PRB 76 054522 (2007)

  22. Symmetry of the Cooper pair (No spin flip) Sign change (MARS) Interface-induced symmetry (subdominant component ) Bulk state • ESE (Even-frequencyspin-singleteven-parity) • ETO (Even-frequencyspin-tripletodd-parity) • OTE (Odd-frequencyspin-tripleteven-parity) • OSO (Odd-frequencyspin-singletodd-parity) ESE (s,dx2-y2 -wave) (1) No ESE + (OSO) (2) OSO +(ESE) ESE (dxy-wave) Yes (3) ETO(px-wave) OTE + (ETO) Yes ETO(py-wave) ETO + (OTE) (4) No (4) (1) (2) (3) Phys. Rev. Lett. 99 037005 (2007)

  23. Contents （１）What is odd-frequency pairing (2)Ballistic normal metal junctions （3）Diffusive normal metal junctions (4）Ferromagnet/Superconductor junctions

  24. Impurity scattering effect Tanaka and Golubov, PRL. 98, 037003 (2007) Ballistic Normal metal Superconductor Only s-wave pair amplitude exists in DN Impurity scattering (isotropic) Diffusive Normal metal (DN) Superconductor (1)ESE (2)OTE ESE (Even-frequencyspin-singleteven-parity) OSO (Odd-frequencyspin-singletodd-parity)

  25. Usadel equation Available for diffusive limit Diffusivelimit Angular average Diffusive normal metal region attached to superconductor

  26. 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

  27. Even frequency spin singleteven parity(ESE) pair potential DN S s-wave case

  28. ー ＋ DN Odd frequency spin triplet s-wave (OTE) pair is induced in DN Px-wave case New type of proximity effect Y.Tanaka, A.A.Golubov, Phys.Rev.Lett. 98, 037003 (2007)

  29. Even frequency spin triplet odd parity (ETO) pair potential ＋ ー DN ー ＋ DN Px-wave case Py-wave case (no proximity& no MARS)

  30. Summary of Proximity effect (diffusive normal metal) Induced pair amplitude in DN Symmetry of the pair potential Even frequency spin singlet even parity (ESE) ESE (1) Even frequency spin triplet odd parity (ETO) (2) OTE Odd frequency spin triplet even parity (OTE) OTE (3) Odd frequency spin singlet odd parity (OSO) (4) ESE

  31. STS STS MARS MARS ZEP No ZEP Diffusive normal Metal (DN) Diffusive normal Metal (DN) Triplet superconductor Singlet superconductor LDOS in DN has a zero energy peak LDOS in DN does not have a zero energy peak How to detect triplet superconductor MARS (Mid gap Andreev resonance state) can penetrate into DN by proximity effect only for triplet superconductor junctions

  32. How to detect odd-frequency paring amplitude: measuring electrical conductivity Asano, Tanaka, Golubov, Kashiwaya, PRL 99, 067005 (2007) Sr2RuO4 Ａｕ:I+ Ａｕ:I- Ａｕ:V+ Ａｕ:V- OTE (Odd-frequency spin-tripleteven-parity) ESE (Even-frequency spin-singleteven-parity) Kashiwaya, Maeno 2007 OTE proximity ESE proximity (conventional) Zero energy peak No Zero energy peak

  33. Contents （１）What is odd-frequency pairing （２）Ballistic normal metal junctions （3）Diffusive normal metal junctions （4）Ferromagnet/Superconductor junctions

  34. Odd-frequency pair amplitude (not pair potential) is generated in ferromagnet junctions Odd frequency spin-triplet s-wave pair spin-singlet s-wave pair _ + Ferromagnet Superconductor Bergeret, Efetov, Volkov, (2001) Eschrig, Buzdin, Kadigrobov,Fominov, Radovic Generation of the odd-frequency pair amplitude in ferromagnet

  35. Spin triplet Cooper pairs in SF systems << triplet Josephson effect in SF multilayered system with noncollinear ferromagnets and thin superconductors

  36. Josephson current in S/HM/S Half metal : CrO2 Keizer et.al., Nature (2006) Bergeret et. al., PRL(‘01), Kadigrobov et. al., Europhys Lett.(‘01) Spin active interface Theory in the clean limit Eschrig et. al., PRL(‘03) Lofwander and Eschrig, Nature Physics (2008)

  37. Recursive GF Furusaki, Physica B(‘92), Asano, PRB(‘01) Advantages SNS, SFS, S/HM/S Parameters : exchange : spin-flip Y.Asano, Y. Tanaka, A.A.Golubov, Phys.Rev.Lett.98, 107002 (2007)

  38. Spin active interface SFS, S/HM/S self-averaging SFS S/HM/S only No sign change odd-frequency pairs

  39. Odd-frequency pairs

  40. Quasiparticle DOS in Half Metal S/HM/S SFS only even-odd mix pure odd Zero Energy Peak can be detected by tunneling spectroscopy

  41. 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))

More Related