Josephson Interferometry:

Transcription

1 Josephson Interferometry: Mapping the Pairing Symmetry of Unconventional Superconductors - - Dale J. Van Harlingen University of Illinois at Urbana-Champaign

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3 Josephson Interferometry: Mapping the Pairing Symmetry of Unconventional Superconductors - - Dale J. Van Harlingen University of Illinois at Urbana-Champaign

4 Donald M. Ginsberg Professor of Physics University of Illinois experimental condensed matter physicist musician, storyteller, poet, mentor, friend

5 Conventional ( classic ) superconductivity BCS theory: Bardeen, Cooper, Schrieffer (1957) k' 1 k 2 q e - e - MECHANISM = attractive phonon-mediated electron-electron interaction Cooper pairing k 1 k' 2 GROUND STATE = superfluid pair condensate ψ = n s e iϕ macroscopic phase coherence EXCITATIONS = normal quasiparticles with an isotropic energy gap k z (k) = s-wave 3 quasiparticle tunneling k y G/G(eV>> ) 2 1 k x ev/

6 Growing Family of Unconventional Superconductors Cuprate superconductors: Organic superconductors: YBa 2 Cu 3 O 7-x T c = 92K κ-(bedt-ttf) 2 Cu[N(CN) 2 ] Br T c = 11.6K d-wave anisotropic d-wave Heavy Fermion superconductors: UPt 3 T ca =.5 T cb =.45K Ruthenate superconductors: Sr 2 RuO 4 T c = 1.5K (k x2 -k y2 ) k z (k x ik y ) 2 k z complex p-wave

7 Pairing Symmetry Roadmap for Experimentalists EVEN PARITY STATES ODD PARITY STATES PAIRING STATE MAGNITUDE RELATIVE PHASE φ isotropic s 1 PAIRING STATE p x 1 MAGNITUDE π RELATIVE PHASE φ π 2 anisotropic s d x 2 -y d x 2 -y 2 i ε s π π 2 π p y - p x i ε p y θ π π 2 π π θ.5 π d x 2 -y 2 i ε d xy π π Complex order parameter broken time-reversal symmetry phase shift δ, π θ θ

8 Experimental tests of the symmetry 1. Parity (even = spin-singlet vs. odd = spin-triplet) NMR Knight shift not always definitive 2. Real vs. complex order parameter muon spin resonance senses spontaneous internal magnetic field Kerr effect 3. Magnitude of order parameter (energy gap) (a) thermodynamic, electrodynamic, optical, tunneling,... experiments that count number of excitations (b) spectroscopies that probe the k-space anisotropy 4. Phase of order parameter (a) quasiparticle tunneling spectroscopy --- sensitive to sign change through formation of zero-energy bound states (b) Josephson interferometry --- sensitive to the phase anisotropy

9 Josephson interferometry: measuring the phase anisotropy the corner SQUID Order parameter alignment Unconventional SC single crystal domains align N-S, not a-b Conventional SC thin film loop dc SQUID (Superconducting QUantum Interference Device) measures the phase shift inside the crystal between orthogonal directions Josephson tunnel junctions tunneling selects direction in k-space Wollman, Ginsberg, Leggett, Van Harlingen (1993)

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11 The corner SQUID experiment s-wave d-wave Critical current Magnetic flux (Φ ) Magnetic flux (Φ ) corner SQUIDs 1µm Observations edge SQUIDs 1-1. π -.5 π. π.5 π 1. π 1.5 π 2. π Phase shift D. A. Wollman, D. J. Van Harlingen, W. C. Lee, D. M. Ginsberg, and A. J. Leggett, Phys. Rev. Lett. 71, 2134 (1993)

12 The corner junction experiment Critical current s-wave d-wave Magnetic flux Magnetic flux Critical current ( µ A) Applied magnetic field (mg) D. A. Wollman, D. J. Van Harlingen, J. Giapintzakis, and D. M. Ginsberg, Phys. Rev. Lett. 74, 797 (1995)

13 Conditions for spontaneous currents --- dc SQUID - - π-phase shift can produce a spontaneous circulating current in a multiply-connected geometry (Bulaevskii) Onset/magnitude depends on the inductance parameter: 2π L Ic β = Φ and the critical current asymmetry parameter: Spontaneous current (I c ) β = 2πLI c Junction phases π π/2 π β = 2πLI c α = I I c1 c1 I I c2 c2 Spontaneous magnetic flux (Φ ) Spontaneous magnetic flux (Φ ) β = 2πLI c β = 2πLI c A. Mathai, Y. Gim, R. C. Black, A. Amar, and F. C. Wellstood, Phys. Rev. Lett. 74, 4523 (1995)

14 The tricrystal ring experiment --- YBCO adjust grain boundary angles so that one segment has a π phase shift spontaneous circulating current Scanning SQUID microscope image 6 75 C. C. Tsuei, J. R. Kirtley, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, T. Shaw, J. Z. Sun, and M. B. Ketchen Phys. Rev. Lett. 73, 593 (1994)

15 Experiment: enhanced magnetic flux in granular BSCCO composites Paramagnetic Meissner Effect W. Braunisch, N. Knauf, G. Bauer, A. Kock, A. Becker, B. Freitag, A. Grütz, V. Kataev, S. Neuhausen, B. Roden, D. Khomskii, D. Colleen, J. Bock, and E. Preisler. Phys. Rev. B 48, (1993) Model: spontaneous supercurrents in multiply-connected d-wave grains Manfred Sigrist and T. M. Rice, Rev. Mod. Phys. 67, 53 (1995)

16 The tricrystal ring experiment --- electron-doped cuprates Nd 1.85 Ce.15 CuO 4-y half-integer vortex trapped at the grain boundary intersection C. C. Tsuei and J. R. Kirtley, Phys. Rev. Lett. 85, 182 (2)

17 Grain boundary junctions Geometry for testing symmetry: 45 -asymmetric junction facets sample different signs of the d-wave order parameter Multi-corner junction Maximum I c not at B=O Symmetric with respect to field polarity S-wave would give Fraunhofer pattern H. Hilgenkamp, J. Mannhart, and B. Mayer, Phys. Rev. B 53, (1996)

18 Cuprate family --- all d-wave, all the time tested vs. material, temperature, carrier doping, magnetic impurities, Phase-sensitive tests of the symmetry of the pairing state in the high temperature superconductors --- Evidence for dx 2 -y 2 symmetry. D. J. Van Harlingen, Rev. Mod. Phys. 67, 515 (1995) Pairing symmetry in cuprate superconductors. C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys. 72, 969 (2)

19 Fragility? of unconventional superconductors s-wave superconductor: scattering does not affect superconductivity Anderson theorem unconventional superconductor: scattering changes magnitude and phase of the order parameter formation of zero-energy bound quasiparticle states suppression of d-wave at interfaces and defects onset of superconducting phases with complex order parameter broken time-reversal symmetry ψ d x 2 -y 2 d x 2 -y 2 id xy s, d xy x d x 2 -y 2

20 Experimental evidence for complex superconducting phases.23 Spontaneous splitting of the zero-bias conductance peak: d dis transition Conductance (S) H= 4.2 K 1.5 K Bias (mv) M. Covington, M. Aprili, E. Paraoanu, L. H. Greene, F. Xu, J. Zhu, and C. A. Mirkin, Phys. Rev. Lett. 79, 277 (1997) Lifting of nodes: drop in thermal conductivity in Nidoped BSCCO: d did transition YBCO Ni-YBCO R. Movshovich, M. A. Hubbard, M. B. Salamon, A. V. Balatsky, R. Yoshizaki, J. L. Sarrao, and M. Jaime, Phys. Rev. Lett. 8, 1968 (1998)

21 Josephson interferomertry of complex order parameters Angle SQUID 1. δ Critical current.5 π/4 π/2 3π/4 π δ = phase shift Magnetic flux (Φ/Φ ) Angle junction δ Critical current π/4 π/2 3π/4 π Magnetic flux (Φ/Φ )

22 Effect of onset of complex order parameter.12 Crtical current I/I c ε =.1 d x 2 -y 2 i ε d xy d x 2 -y Applied magnetic flux Φ/Φ Onset of secondary order parameter: * increases B= critical current node lifted * breaks polarity symmetry broken time-reversal symmetry

23 YBCO grain boundary junction Ic/Ic() T=13K T=4.2K T=1.4K Critical Current (µa) K 9.K 6.4K 1.5K Applied magnetic field (G) Applied Magnetic Field (G) No evidence for subdominent order parameter (< 1%) W. K. Neils and D. J. Van Harlingen, Phys. Rev. Lett. 88, 471 (22)

24 Ni-doped YBCO grain boundary junction Critical Current (µa) K.7K 3K 1K 22K Critical Current (µa) K 1mK Applied Magnetic Field (G) Applied Field (Gauss) Conclusion: the d-wave order parameter is very robust

25 New developments --- edge junction technology Edge overgrowth technique Reliable junctions between HTSC and conventional SC can make many junctions and any angle H.J.H. Smilde, H. Hilgenkamp, G. Rijnders, H. Rogalla and D.H.A. Blank, Appl. Phys. Lett. 8, (22)

26 Map phase variation --- lobe asymmetry J.R. Kirtley,C.C. Tsuei, Ariando, C.J.M. Verwijs, S. Harkema, H. Hilgenkamp, Nature Physics 2, 19 (26)

27 The Quest for Complex Superconductors Heavy Fermion superconductors: UPt 3 T ca =.5 T cb =.45K Ruthenate superconductors: Sr 2 RuO 4 T c = 1.5K (k x2 -k y2 ) k z (k x ik y ) 2 k z complex p-wave

28 Ruthenate superconductor: Sr 2 RuO 4 (Y. Maeno, 1994) perovskite structure but Cu-free (T c = 1.5 K) close to a ferromagnetic transition electrodynamics strongly non-local (ξ ~ λ) suspected to be unconventional suspected to be p-wave suspected to break time-reversal symmetry suspected multiple superconducting bands Proposed order parameter: complex p x ip y state (M. Rice and M. Sigrist) 2D analogue of 3 He A-phase k y Isotropic energy gap (magnitude) π/2 k x 3π/2 Continuous linear phase variation Broken time-reversal symmetry π p x ip y π p x -ip y Possibility of chiral domains 3π/2 π/2

29 The Parity Problem Josephson Coupling of EVEN (singlet) and ODD (triplet) Superconductors THEORY 1st order Josephson effect cancels - 2nd order Josephson effect allowed: weak coupling ~ T 4 distinguishable by Shapiro steps EXPERIMENT Spin-orbit scattering breaks spin symmetry net supercurrrent possible INTERFEROMETRY - Could couple to either lobe bi-modal results ( or π phase shift) Domain structure nucleation at surface K. D. Nelson, Z. Q. Mao, Y. Maeno, and Y. Liu, Science 36, 5699 (24)

30 Josephson phase interferometry s-wave d-wave δ= δ=π - - Fraunhofer diffraction pattern Minimum at zero field δ=π/2 Chiral p-wave δ=π Grain boundary Polarity asymmetry Multiple phase interference Chiral domains

31 Critical current switching noise in SRO junctions Hysteresis 6 Abrupt switches Voltage(µV) Critical current (ma) Applied flux (mg) Applied field (G) -25 Telegraph noise (vs. field) -1 Telegraph noise (vs. time) Voltage (µv) Voltage (µv) Applied field (mg) Time (s)

32 Chiral order parameter domains Francoise Kidwingira, J. D. Strand, D. J. Van Harlingen, Yoshiteru Maeno, Science 314, 1267 (26) p x ip y p x -ip y Evidence for domains Phase interference explains variety of diffraction patterns Switching between different domains configurations Hysteresis caused by domain wall motion and pinning Chiral currents flow around domain edges --- estimated domain size ~ 1µm Energy competition for domains formation: GAIN = lower chiral field energy COST = Josephson domain wall energy ~ cos(φ) Not observed by SSM: J. R. Kirtley, C. Kallin, C. W. Hicks, E.-A. Kim, Y. Liu, K. A. Moler, Y. Maeno, and K. D. Nelson Phys. Rev. B 76, (27)

33 Diffraction patterns: chiral domains δ = Critical current (I/I ) Magnetic flux (Φ /Φ ) δ = π Simulation (1 domains) Critical current (I/I ) Magnetic flux (Φ /Φ ) Critical current (ma) Applied field (G) Measurement Critical current (µa) Applied field (mg)

34 Sensitivity to single domain switching Motion of a single domain wall dramatically changes the critical current diffraction pattern accounts for switching noise observed Configuration A I c /I c Configuration A Configuration B ConfigurationB I c /I c Magnetic flux (Φ/Φ )

35 Field cooling: critical current enhancement 1 3µG field Cooled Critical current (µa) Zero field Cooled Critical current (µa) Applied field (mg) Applied field (mg) 1-3µG field Cooled 8 Enhancement only for limited field range because of vortex trapping Dramatic increase in I c for both polarities Field range scales with junction size but is surprisingly small (< 1mG) Critical current (µa) Applied field (mg)

36 Field cooling: domain training and memory effects Critical current (µa) Critical current increases gradually with successive field-cooling cycles Possible mechanism: domain alignment can be trained by applied field Zero-field cooled Critical current (µa) Field cooled Cycle #1 Critical current (µa) Field cooled Cycle # Applied field (mg) Applied field (mg) Applied field (mg) Critical current (µa) Critical current retains enhancement after zero-field cooling, decays over time Possible mechanism: antiferromagnetic inclusions (Sr 3 Ru 2 O 7 ) or surface states Field cooled Critical current (µa) Zero-field cooled Immediately after field-cooling Critical current (µa) Zero-field cooled 24 hours after field-cooling Applied field (mg) Applied field (mg) Applied field (mg)

37 Chiral triplet superconductor? heavy fermion UPt 3 Two superconducting phases: hexagonal structure upper-phase real (k x2 -k y2 ) k z lower-phase complex (k x ik y ) 2 k z UPt 3 epoxy In Pb Current (µa) Voltage (nv) Critcal current (µa) T cu ~.5K Temperature (mk) Critcal current (µa) T cl = T cu 5mK S L S U N Temperature (mk)

38 UPt preliminary diffaction patterns T = 41mK Sweep 1 Sweep mK 42mK 44mK 46mK 48mK 5mK I C (µa) I C (µa) Flux (mg) Flux (mg) Complicated but not at all like Sr 2 RuO 4 Patterns retrace --- no hysteresis, no switching noise Patterns at fixed temperature are reproducible Patterns at different temperatures are dramatically different! evidence for magnetic surface states or domains?

39 Applications of Josephson interferometry? --- Qubits 1. Provides natural and precisely-degenerate two-level system E J Φ Spontaneous circulating current in rf SQUID Precisely-degenerate two-level system with no flux bias 2. Non-Abelian states in chiral superconductors (Sr 2 RuO 4 ) for topological quantum computing