1 / 38

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

dalmar
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. Odd-frequency pairing even-frequency superconductivity Fermi-Dirac statistics D(w) D(ω), f(ω) Symmetry ofpairwave functions: MomentumxSpinxFrequency w odd-frequency superconductivity Berezinskii (1974): D(ω), f(ω) Spin-triplet s-wave Balatsky&Abrahams (1992): Spin-singlet p-wave w

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

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

  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. Odd-frequency pairing state is possible in inhomogeneous superconductors even for conventional even-frequency paring in the bulk Broken spin rotation symmetry or spatial invariance symmetry can induce odd-frequency pairing state: -ferromagnet/superconducor junctions: Bergeret,Volkov&Efetov, 2001 - non-uniform systems: Junctions: Tanaka&Golubov, 2007; Eschrig&Lofwander, 2007 Vortices: Yokoyama et al., 2008; Tanuma et al., 2009)

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

  10. 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)

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

  12. spin-triplet p-wave superconductor Normal metal

  13. 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)

  14. 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.

  15. Andreev bound states in inhomogeneous systems are manifestations of odd-frequency pairing amplitude Andreev bound states Positive pair potential Electron-like QP Cooper pair Hole-like QP Negative pair potential Surface: Tanaka et al, 2007 Vortex : Tanuma et al, 2009 Scattering direction of QP Phase change due to a vortex

  16. 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)

  17. 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)

  18. 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

  19. 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)

  20. 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)

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

  22. 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)

  23. 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

  24. 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)

  25. Density of states in DN Conventional proximity effect with Even-frequency Cooper pair in DN Unconventional proximity effect with Odd-frequency Cooper pair in DN Tanaka&Kashiwaya, 2004

  26. Summary of Proximity effect (diffusive normal metal, s-wave pairing state only) 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

  27. 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

  28. Andreev bound states in inhomogeneous systems are manifestations of odd-frequency pairing amplitude Andreev bound states Positive pair potential Electron-like QP Cooper pair Hole-like QP Negative pair potential Surface: Tanaka et al, 2007 Vortex : Tanuma et al, 2009 Scattering direction of QP Phase change due to a vortex

  29. Symmetry of the Cooper pair in a vortex core Center of the vortex core l; angular momentum m; vorticity bulk Even ESE Even ESE (s-wave..) Even Odd ESE (s-wave..) OSO Odd Even ETO (chiral p-wave) ETO Odd Odd ETO (chiral p-wave) OTE ESE (Even-frequencyspin-singleteven-parity) ETO (Even-frequencyspin-tripletodd-parity) OTE (Odd-frequencyspin-tripleteven-parity) OSO (Odd-frequencyspin-singletodd-parity Yokoyama et al., Physical Review B, Vol. 78, 012508, 2008

  30. Difference of the angular momentum of the odd-frequency pair at the core center Angular momentum at the center of core; l+m l: angular momentum m: vorticity Tanuma, Hayashi, Tanaka Golubov Phys. Rev. Lett. 102, 117003 (2009). Chirality and vorticity: Y. Kato and N. Hayashi (2000, 2001,2002)

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

  32. 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

  33. 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)

  34. 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)

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

  36. Odd-frequency pairs

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

  38. Summary • Ubiquitous presence of the odd-frequency pairs in inhomogeneous systems. • Low energy Andreev bound states can be expressed in terms of odd-frequency pairing (proximity effect and vortices). • The origin of the anomalous proximity effect in DN/spin-triplet p-wave junction is the generation of the odd-frequency pairing state. (4) Odd-frequency triplet pairs carry supercurrent in S/Half Metal/S Josephson junctions.

More Related