Andreev bound states in anisotropic superconductor junctions

Transcription

1 Andreev bound states in anisotropic superconductor junctions S. Kashiwaya AIST Y. Tanaka Nagoya University Collaborators AIST Tokyo Univ of Sci. Hokkaido Univ. Kyoto Univ. H. Kambara, H. Kashiwaya, T. Matsumoto T. Furuta, H. Yaguchi Y. Asano Y. Maeno 1 Scope of this conference 2 Experiments on Sr 2 RuO 4

2 Scope of this conference Phenomena Physics Materials Andreev Reflection & Coherence of QP's A4,A5,A6, B1, B3, B4, B5, B6 Ferromagnetic & spin related effects A7,A8,A9,A10, B2 Odd frequency pairing A11,A12 Topological superconductor B8,B9,B10 Chiral p-wave superconductors A1,A2,A3 Iron pnictide B11,B12,B13 Vortex physics A13,B7,B14 New direction of superconducting nanostructure

3 electron Andreev reflection An elemental scattering process at S/N interface electron Cooper pair Fermi energy Energy gap hole Normal metal Superconductor 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 reflection 1 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 BTK formula (Blonder et al, 1982) Conductance of this junction is described by σ ev F ( ) a b a b 2 2 Amplitude of Andreev reflection Amplitude of normal reflection

4 Andreev bound states The spatial variation of pair potential yields quasi-particle bound states in superconductors. Superconductor Cooper pair electron Normal metal Superconductor Cooper pair hole φ 1 φ 2 1 The electron (E< ) in the normal metal cannot enter into both sides of superconductors as the quasiparticle Energy level of bound states as the function of phase difference 1 2 They form discrete bound states by repeating the multiple Andreev reflection at S/N boundaries φ + φ phase difference Zero-energy bound states at the phase difference of π

5 Long standing issues: ABS related phenomena DC Josephson Current: ABS carries Josephson current electron l Vortex core states H. F. Hess, 1990 Cooper pair Cooper pair hole SNS junction Ishii, 1979 All these phenomena have the same origin! Andreev reflection and ABS Zn impurity in Bi2212 Pan, 2001 ABS around impurity DeGennes-Saint James bound states N S ABS in normal metal side of Clean normal metal/s-wave

6 Surface Andreev bound states in anisotropic superconductors In the case of anisotropic superconductors, pair potentials of different phases and amplitudes are interfolded in momentum space. Bound states are formed at the surface + Surface scattering d xy -wave pair potential - Hu, 1994, Tanaka, Kashiwaya, 1995 Localized zero-energy ABS Pair potential depth Ru-Oxide SrRuO4 (Mao, Yaguchi) Organic κ-(bedt-ttf)2cu[n(cn)2]br (Ichimura) Heavy Fermion UBe13 (Ott) CeCoIn5 (Wei)

7 Scope of this conference Phenomena Physics Materials Andreev Reflection & Coherence of QP's A4,A5,A6, B1, B3, B4, B5, B6 Ferromagnetic & spin related effects A7,A8,A9,A10, B2 Odd frequency pairing A11,A12 Topological superconductor B8,B9,B10 Chiral p-wave superconductors A1,A2,A3 Iron pnictide B11,B12,B13 Vortex physics A13,B7,B14 New direction of superconducting nanostructure

8 General description of Cooper pair In recent theoretical works, the physical origin of ABS is becoming more clearer. r r Pair amplitude F k, ω) cˆ r cˆ r = Φ( k, ω) χ( s, s' ) ss' ( = ks ks' orbital frequency Pair amplitude Fss (k) must be an odd function with respect to the permutation of electrons. spin Conventional consensus of Cooper pairs Even for ω Spin Orbital odd-even singlet s-wave, singlet d-wave even-odd triplet p-wave, triplet f-wave Even Frequency pair potential Gapped states Recent improvement clarified Odd for ω Spin Orbital odd-odd singlet p-wave, singlet f-wave even-even triplet s-wave, triplet d-wave Odd Frequency pair potential Ungapped states Berezinskii, Balatsky-Abrahams, Abrahams-Balatsky-Schrieffer-Allen, Vojta-Dagotto

9 Possible symmetry conversion in proximity effect Odd frequency pairs are easily produced from even frequency pairs through symmetry breaking. Real space: Edge, non-magnetic impurity, non-uniformity Tanaka, 2006 Momentum related conversion even odd even even triplet p-wave even-freq triplet s-wave odd-freq Spin space: Spin active interface, spin flip scattering Bergeret, Volkov, Efetov, 2001 odd even singlet s-wave even-freq Spin related conversion even even triplet s-wave odd-freq

10 Ubiquitous presence of odd-frequency pairing states Odd frequency component is ubiquitously exist in non-uniform superconductors. The ratio of pair potential amplitude of even and odd S-wave Clean normal metal Odd-frequency pairing Even-frequency pairing Coincide with DeGennes-Saint James bound states Y. Tanaka, Y. Tanuma A.A. Golubov, PRB (2007) DeGennes-Saint James bound states are composed of odd frequency pairing states. Odd frequency pairs were treated unconsciously in old problems.

11 Back to the surface ABS case Reinterpretation of zero-energy ABS Even frequency Even parity Tanaka, Odd frequency Odd parity x Even frequency component Odd frequency component Gapped states Ungapped states ZBCP at d xy -surface is reinterpreted as odd frequency pairing component induced by the scattering at the interface. Close correlation between ABS and odd frequency pairing is becoming clearer.

12 Experimental results: anomalous Josephson current in CrO 2 R. S. Keizer, et al, 2006 Josephson current through half metallic ferromagnet CrO 2 Bergeret, Volkov, Efetov, 2001 Possible explanation Asano Nb even freq. s-wave spin active interface even freq. s-wave CrO 2 odd freq. s-wave We expect a lot of novel phenomena will be discovered through odd frequency research.

13 How to detect odd frequency proximity effect more clearly? 1 Spectroscopy of DN/Px Odd freq. component has zero-energy peak in DOS px DN STM tip LDOS(Normalized) 4 2 p wave Josephson effect of Px/DN/Px Anomalous temp. dep. due to odd px DN px 3 Transport experiments Asano, 2007 P-wave superconductor is suitable for these purposes. We expect p-wave micro-devices will be studied more in detail.

14 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. d xy,wave Chiral p-wave Non-centrosymmetric superconductors (Helical) k k k Chiral gapless edge states Spontaneous current at edge Spin current No net edge current Analogy Integer quantum Hall system Quantum spin Hall system These three types have different surface ABS topology. Topology related new physics coming out from the topology of gap function.

15 New materials and functionality 1 Iron Penictide Tc 55K Pairing mechanism? Hosono group New functionality Superconductor-based LE : π junction in SFS for Qubit Suemune, Takayanagi S /F/ S

16 Scope of this conference Phenomena Physics Materials Andreev Reflection & Coherence of QP's A4,A5,A6, B1, B3, B4, B5, B6 Ferromagnetic & spin related effects A7,A8,A9,A10, B2 Odd frequency pairing A11,A12 Topological superconductor B8,B9,B10 Chiral p-wave superconductors A1,A2,A3 Iron pnictide B11,B12,B13 Vortex physics A13,B7,B14 We will find New direction of superconducting nanostructure through these discussions

17 Transport properties in microfabricated Sr 2 RuO 4 devices Maeno, 1994 Superconducting states of Sr 2 RuO 4 Layered perovskite d = 0 z (k x ± ik y ): chiral p-wave Equal spin pair d//z Orbital moment (L z = 1or-1) This material best to study 2D chiral p-wave physics! Quasi-2D Fermi surface

18 Mesoscopic Sr 2 RuO 4 devices Sr 2 RuO 4 is unique material with complex order parameter, we expect novel functionalities in ruthanate microdevices. Unfortunately, no thin film of superconducting Sr 2 RuO 4 Then we develop novel microfabrication process by using FIB from single crystals. 70 µm Sr 2 RuO 4 single crystal I- I+ V- V+ Au FIB We have already fabricated various types of ruthanate based microdevices, Weak link bridge C-axis junction T-shape junction SQUID 20µ 20µ 3.5µ 5µ

19 Details are presentd in H. Kambara, next talk. Advantages of FIB process compared with conventional lithography process Intrinsic junction Bi2212 d-wave 1 Applicable for various superconductors even without thin films 2 3-Ddevice fabrication is possible. Bi 2 Sr 2 CaCu 2 O 8+δ l c >ξ c Tunneling Intrinsic junction of Sr 2 RuO 4 p-wave Sr 2 RuO 4 l c <ξ c Weak link V (µv) T = 1.0 K I (ma)

20 Targets of Sr 2 RuO 4 today's presentation 1 Clarify the transport properties of weak link Critical current in bridges Novel switching due to chiral domain wall motion More details H.Kambara, next talk 2 Detect of vortex states using SQUID's Searching for predicted half vortex quantum Future application :Topological quantum computing

21 Typical properties of in-plane Sr 2 RuO 4 bridge FIB image R / R 4.2K R-T 3-K (c199-4) T (K) (dv/di) / (dv/di) 4.2 K dv/di-i 3-K (c199-4) (08/3/3-5) I (ma) I c 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 CAL_080303IV_4.2K_PU.DAT CAL_080303IV_1.8K_PU.DAT CAL_080303IV_1.7K_PU.DAT CAL_080303IV_1.6K_PU.DAT CAL_080303IV_1.5K_PU.DAT CAL_080305IV_4.2K.DAT CAL_080305IV_3.0K_PU.DAT CAL_080305IV_2.5K_2.DAT CAL_080305IV_2.2K_2.DAT CAL_080305IV_2.0K.DAT Magnetic field response of dv/di B[gauss] I c0 (ma) c199-8 FIB (20*6*6) FIB (10*3*6 (center)) Conventional I c -T I [ma] Ic suppression due to magnetic field T/T c0 All these features are mostly consistent weak link type Josephson junctions (JJ) Thus we believe weak link JJ's of ruthante are successfully fabricated.

22 Anomalous feature : bridge size dependence of I c, J c S Necking In conventional case, L W S = Wt I // ab t: thickness Resistance R bridge L = ρ S Ic = J c S Conventional behavior in Nb thin films (Ic ~ J c S) conventional Critical current density: J c S

23 L / R bridge (m/ω) Anomalous J c enhancement in Sr 2 RuO 4 bridges Resistance shows conventional dependence c199-4 c c199-8 c199-9 c359-2 c359-7 thickness width conventional No problem in fabrication In the case of the smallest junction, J c is two order of magnitude enhanced as compared to known bulk value. I c0 (normalized) T = 4.2 K I c tends to be insensitive to S conventional c199-4 c c199-8 c199-9 c359-2 c [ 10-9 ] J c (A/cm 2 ) c199-4 (1.4 K) c (1.3 K) c199-8 (1.2 K) c199-9 (1.3 K) c359-2 (1.4 K) c359-7 (1.3 K) Unusual! J c (0) = 500 A/cm 2 for bulk pure Sr 2 RuO 4 (by Deguchi and Maeno) S (µm 2 ) [ 10 3 ]

24 What is the origin of J c enhancement? Conventional explanation: non-uniformity of J c due 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) J c enhancement in experiments is far larger than expected Grenko, (2002) Possible explanation: high current channel formation along edge Supercurrent only along edge? necking I c almost constant against the necking High Jc edge channel formation! But the origin this channel is unclear. A links to chiral gapless edge states? The influence of edge channel appear as hysteresis in I-V H. Kambara, next talk

25 Detection of vortex in 2D chiral p-wave superconductor Differently from conventinal s-wave superconductors, vortex in multi-component superconductors can take fractional form. Most plausible pair potential form ) d( k) = 0d x y k ( k ± ik ) exp( iϕ ) ) Maeno, 2003 d-type spin orbital Two types of half quantum vortex in principle. l-type d-vector φ 1, φ2 =, l-vector φ 1, φ2 = k x, ik y k x +ik y l-string Φ 0 /2 k x -ik y Φ 0 /2 Volvik, 1998 Ivanov, 2001 d-vector d-string Ichioka, et al Φ 0 /2 Φ 0 /2

26 Stability of HQV's E=E halfpair -E full 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.

27 How to detect HQV's in Sr 2 RuO 4. Magnetic field modulation of SQUID Conventional s-wave DC-SQUID shielding current B= n Φ Periodicity is Φ 0 /S conventional -1 1 Φ/ Φ 0 Chiral p-wave DC-SQUID with stable HFQ B= n Φ 0 /2 Periodicity is Φ 0 /2S? Φ 0 / 2 Φ 0 / 2 01/21 Φ Φ/ Φ 0

28 FIB images Fabrication of Sr 2 RuO 4 SQUID and temperature dependence and dv/di K (c199-20) -3 (09/8/13) I mod = 87 µa cooling warming R-T R (Ω) (dv/di) / (dv/di) 4.2 K, 0 ma T (K) dv/di-i 3-K (c199-20) -3 (09/8/13) 1.3 K K K K K K I (ma) 1.0 K K-1 Expected I c modulation cycle (Φ 0 ) is 0.7 gauss I c

29 Magnetic field response of Sr 2 RuO 4 SQUID Mapping of dv/di Mapping of dv/di B[gauss] B[gauss] I c I c Flux trap? 0-3G 1.3K I [ma] 50-53G 1.1K I [ma] Weak modulation of I c but not periodic I c jump possibly due to flux trap No periodic modulation of I c 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.

30 Summary 1 We develop a fabrication technique for µm-size Sr 2 RuO 4 devices using FIB process. 2 We found the high current density edge mode in Sr 2 RuO 4 bridges. It is unclear whether this is peculiar to chiral p-wave superconductors. 3 Magnetic field responses of I c in Sr 2 RuO 4 SQUID didn't show I c modulation to the applied field. Not succeeded in detecting HVQ's. More details of SRO bridges will be presented by H.Kambara, next talk