Odd frequency pairing in q y p g superconducting heterostructures - PowerPoint PPT Presentation

Odd frequency pairing in q y p g superconducting heterostructures p g Alexander Golubov Twente University, The Netherlands Twente University The Netherlands Y. Tanaka Nagoya University Japan Nagoya University, Japan Y. Asano Hokkaido University, Japan Y Tanuma Y. Tanuma Akita University, Japan

Contents Contents （１） What is odd-frequency pairing （２） Normal metal / Superconductor junctions （３） Vortices in superconductors （３） Vortices in superconductors

Conventional Classification of Symmetry of Cooper pair Symmetry of Cooper pair Spin-singlet Cooper pair Spin-singlet Cooper pair Even Parity Even Parity d-wave Cuprate p s-wave BCS Spin-triplet Cooper pair Odd Parity y 3 He p-wave Sr 2 RuO 4

Odd-frequency pairing even-frequency Fermi-Dirac statistics  (  )  ( ω ), f( ω ) superconductivity Symmetry of pair wave functions: y y p Momentum x Spin x Frequency   odd-frequency superconductivity Berezinskii  ( ω ), f( ω ) ( ) ( ) (1974): Spin-triplet s-wave Balatsky&Abrahams  (1992): Spin-singlet p-wave

Odd-frequency pairing state q y p g (1)Odd-frequency pairing (pair potential, gap function) in uniform bulk system (odd-frequency superconductor) if b lk t ( dd f d t ) Uniform (bulk) system: Uniform (bulk) system: electron-interaction Pair amplitude Pair potential p Energy Gap (2)Odd freq enc pairing state (pair amplit de) in (2)Odd-frequency pairing state (pair amplitude) in superconducting junctions

Normal metal Superconductor pair amplitude F pair potential       (  T F i ) Weak coupling BCS: m m

Pair amplitude Pair amplitude (pair correlation) Exchange of two electrons F Fermi-Dirac statistics i Di t ti ti

P i Pair amplitude lit d Exchange of time Even-frequency pairing (conventional pairing) Odd-frequency pairing

Symmetry of the pair amplitude + symmetric,  anti-symmetric + t i ti t i Frequency Spin Spin Orbital Orbital Total Total （ time)   singlet)  BCS  singlet) +(even) +(even) ESE ESE +(even) +( ) Cuprate  (odd)  3 He +(even) +(even) + (triplet) + (triplet) (odd) ETO ETO Sr 2 RuO 4  odd)  +  triplet)  +(even) ( ) OTE p )  odd)   singlet)  (odd)  OSO 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

Previous studies of odd-frequency pairing i i B lk t t Bulk state (Pair potential, Gap function) (P i t ti l G f ti ) Berezinskii (1974) Balatsky, Abrahams, Schrieffer, Scalapino(1992-1993) B l t k Ab h S h i ff S l i (1992 1993) Zachar, Kievelson, Emery (1996) Coleman Mirranda Tsvelik (1997) Coleman, Mirranda, Tsvelik (1997) Vojta, Dagotto (1999) Fuseya Kohno Miyake (2003) Fuseya, Kohno, Miyake (2003) Shigeta, Onari, Yada, Tanaka (2009) Junction (No pair potential) Junction (No pair potential) Induced odd-frequency pair amplitude in ferromagnet attached to spin singlet s wave superconductor attached to spin-singlet s-wave superconductor Bergeret, Efetov, Volkov, (2001)

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

Contents Contents （１） What is odd-frequency pairing (2) Ballistic normal metal junctions (2) Ballistic normal metal junctions (3 ） Vortices in superconductors

Ballistic junction Ballistic junction Ballistic Superconductor Superconductor Normal metal (semi-infinite) (semi-infinite) Y. Tanaka, A. Golubov, S. Kashiwaya, and M. Ueda Phys. Rev. Lett. 99 037005 (2007) y ( ) M. Eschrig, T. Lofwander, Th. Champel, J.C. Cuevas and G. Schon . sc g, . o wa de , . C a pe , J.C. Cuevas a d G. Sc o J. Low Temp. Phys 147 457(2007)

Eilenberger equation (explicitly denote direction of motion) Pair potential Pair potential Quasiparticle function Form factor Pair amplitudes Bulk state Only S S ballistic N normal normal metal x 0

spin-triplet p-wave spin-triplet p-wave Normal metal superconductor

Symmetry of the bulk pair potential is ETO (low-transparent) Pair potential (high-transparent) p x -wave component of ETO pair amplitude s-wave component of OTE pair amplitude s-wave component of OTE pair amplitude ETO (Even-frequency spin-triplet odd-parity) OTE (Odd-frequency spin-triplet even-parity) Y. Tanaka, et al PRL 99 037005 (2007)

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

Andreev bound states in inhomogeneous systems are manifestations of odd-frequency pairing amplitude Andreev bound states Positive pair potential Electron like QP 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

Mid gap Andreev 4 resonant (bound) state S rmalized DOS (MARS) 2 Nor 0 –1 0 1   Local density of state has a zero energy Local density of state has a zero energy peak. (Sign change of the pair potential at the ー ー ＋ ＋ interface) Tanaka Kashiwaya PRL 74 3451 (1995), ー Rep. Prog. Phys. 63 1641 (2000) Buchholz(1981) Hara Nagai(1986) ー Hu(1994) Matsumoto Shiba(1995) Hu(1994) Matsumoto Shiba(1995) Ohashi Takada(1995) Interface (surface) Hatsugai and Ryu (2002)

Superconducting Materials where MARS is observed MARS i b d YBa C O YBa 2 CuO 7-  (Geerk, Kashiwaya, Iguchi, Greene, Yeh,Wei..) (Geerk Kashi a a Ig chi Greene Yeh Wei ) Bi 2 Sr 2 CaCu 2 O y (Ng, Suzuki, Greene….) La 2-x Sr x CuO 4 (Iguchi) L S C O (I hi) La 2-x Ce x CuO 4 (Cheska) Pr 2-x Ce x CuO 4 (R.L.Greene) Sr 2 RuO 4 (Mao, Meno, Kawamura,Laube)  (BEDT-TTF) 2 X, X=Cu[N(CN) 2 ]Br (Ichimura) UBe 13 (Ott) CeCoIn 5 (Wei Greene) PrOs 4 Sb 12 (Wei) Superfluid 3 He (Okuda, Nomura, Higashitani, Nagai)

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

Ratio of the pair amplitude in the N region (odd/even) region (odd/even) At some energy, odd-frequency component can exceed over even frequency one over even frequency one. Odd frequency pairing Odd-frequency pairing Even-frequency pairing Hidden odd frequency component in the 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 i t f d th b d t t l l Bound states condition (Z=0) Bound states condition (Z=0) （ McMillan Thomas Rowell) Odd-frequency pairing Even-frequency pairing E f i i Bound states are due to the generation of the odd-frequency C Cooper pair amplitude i lit d Y. Tanaka, Y. Tanuma and A.A. Golubov, PRB 76 054522 (2007)

Symmetry of the Cooper pair (No spin flip) Sign change Interface-induced symmetry Bulk state (MARS) (MARS) (subdominant component ) (subdominant component ) ESE (s,d x2-y2 -wave) No (1) ESE + (OSO) (2) (2) OSO +(ESE) OSO +(ESE) ESE (d xy -wave) ESE (d Yes Yes ) (3) ETO (p x -wave) OTE + (ETO) Yes ETO ETO (p y -wave) ETO + (OTE) ETO + (OTE) (4) (4) No (4) (1) (2) (3) • 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) OSO (Odd f i i l t dd it ) Phys. Rev. Lett. 99 037005 (2007)

Contents Contents （１） What is odd-frequency pairing (2) Ballistic normal metal junctions (2) Ballistic normal metal junctions (3 ） Vortices in superconductors

Andreev bound states in inhomogeneous systems are manifestations of odd-frequency pairing amplitude Andreev bound states Positive pair potential Electron like QP 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