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Superconductivity and Superfluidity *

Superconductivity and Superfluidity *. Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook: Phenomenological description Superconducting and superfluid systems Generalized microscopic description.

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Superconductivity and Superfluidity *

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  1. Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook: Phenomenological description Superconducting and superfluid systems Generalized microscopic description * D. Einzel, Lexikon der Physik, Spektrum Akademischer Verlag, Heidelberg, 2000

  2. Motivation: Physics Nobel prize 2003 Vitalii L. Ginzburg (born 1916) P. N. Lebedev Physical Institute Moscow Alexei A. Abrikosov (born 1928) Argonne National Laboratory, USA Anthony J. Leggett (born 1938) University of Illinois at Urbana-Champaign, USA

  3. Phenomenological description: London vs. Ginzburg-Landau QM particle with mass M, charge Q, density Ns in external el.mag. Potentials Quantum-mechanical condensate wave function F. und H. London, 1935, Max von Laue, 1938, V. L. Ginzburg und L. L. Landau, 1950 Schrödinger equation charge- supercurrent Neutral mass supercurrent Application: pairs

  4. The London theory does not explain: Merits of the London theory Persistent currents Magnetic field screening Fluxoid quantisation Josephson effects Gauge invariance Q=2e Microscopic origin of Ns Non-local effects Flux lines Interfaces Ginzburg-Landau- and Abrikosov Theory (V. Ginzburg and L. Landau, 1950, A. Abrikosov, 1956) Merits of the Ginzburg-Landau- and Abrikosov theory The Ginzburg-Landau- and Abrikosov theory does not explain: Q=2e Microscopic origin of Ns Behavior at lower temperatures T<<Tc All London results Non-local effects Distinction: type-I and type-II Flux line lattice Arbitrary boundary conditions Thousands of citations

  5. Superconducting and superfluid systems

  6. Superconducting and superfluid systems (ctd.)

  7. Current relaxation in normal Fermi liquids Charged Fermions in metals Drude‘s law momentum relaxation: impurities, Phonons... Neutral Fermi liquids Hagen- Poiseuille‘s law momentum conservation (exception: walls)

  8. Indications of superconductivity: Vanishing resistance Heike Kamerlingh-Onnes, 1911 Indications of superfluidity: Vanishing shear viscosity (?) J. M. Parpia, D. Einzel., 1987 viscosity paradox

  9. „GUT“ of superconductivity and superfluidity charged neutral Fermi Bose spin singlet spin triplet even parity odd parity BCS „non-BCS“ conventionel unconventionel Aspects and systems to be unified: pair correlated Fermi systems weak coupling limit parabolic bands in D=3 und D=2 Restrictions:

  10. BCS mean field treatment of superconductivity and superfluidity Pair attraction near the Fermi surface Spontaneous pair formation in k-space: pair (Gor‘kov-) amplitude Pair potential (energy gap) Broken gauge symmetry

  11. Classification of pair potentials A. Spin structure Pauli principle: Singlet (s=0): even parity Triplet (s=1): odd parity

  12. Unconventional pairing has lower symmetry as the Fermi surface; additional broken symmetries Examples: see next slide Classification of pair potentials (ctd.) B. Orbital structure Conventional pairing shares the symmetry of the Fermi surface; only gauge symmetry broken Examples: classical singlet SC‘s like Hg, Al, V, ...

  13. The broken lattice symmetry in cuprates (Moritz, 11 years)

  14. Conventional and unconventional model pairing states: S=0: singlet S=1: triplet

  15. The d-wave controversy in the High-Tc community PHYSICS TODAY MAY 1993 IN HIGH-TC SUPERCONDUCTORS, IS d-WAVE THE NEW WAVE? BARBARA GOSS-LEVI PHYSICS TODAY PHYSICS TODAY FEBRUARY 1994 IN EXPLAINING HIGH-TC, IS d-WAVE A WASHOUT? PHILIP W. ANDERSON PRINCETON UNIVERSITY

  16. BCS mean field treatment of superconductivity and superfluidity (ctd.) Hamiltonian for spin singlet pairing (triplet pairing: A. J. Leggett, 1965) Nota bene: the energy or Nambu space (Yoishiro Nambu, 1962) is a matrix in particle-hole space Nota bene: spontaneous pair formation „off-diagonal long range order“ (ODLRO)

  17. Bogoliubov-Valatin- diagonalisation Excitation spectrum of Bogoliubov- quasiparticles 0 Quasiparticle Hamiltonian n(xp) Momentum distribution of Bogoliubov- quasiparticles n(Ep) x/kT

  18. Linear response of the quasiparticle system Thermally activated vs. nodal quasiparticles Zeeman Ampere External perturbations Thermal excitations in local equilibrium temperature vector potential temperature change magnetic field

  19. Linear response of the condensate (BCS-Leggett theory) Macroscopic limit Broken gauge symmetry Charge supercurrent Broken spin-orbit symmetry (SBSOS) Leggett, 1971 New: spin supercurrent

  20. C(T)/CN(T) Heat capacity of Bogoliubov- quasiparticles isotropic 2 axial 1 B1g, E1g, E2u 0 0 1 T/Tc

  21. c(T)/cN axial pseudoisotropic B1g, E1g E2u isotropic 0 T/Tc 1 Spin susceptibility of Bogoliubov- quasiparticles 1 0

  22. dlLm(T)/lLm(0) Bogoliubov quasiparticle current and magnetic field penetration depth 1 B1g E1g( ) E2u E1g(||) isotropic 0 0 T/Tc 1

  23. The unconventional superconductivity in UPt3 (J. A. Sauls et al., 1996) singlet even parity (E1g) triplet odd parity (E2u)

  24. Selected experimental results A. Quasiparticle heat capacity UBe13 (H.-R. Ott et al., 1983) Vanadium and Tin

  25. Selected experimental results (ctd.) A. Quasiparticle heat capacity YBa2Cu3O7 (Junod et al., 1996) Sr2RuO4 (Deguchi et al., 2000) C(T)/CN(T) T[K]

  26. Selected experimental results (ctd.) B. Quasiparticle spin susceptibility Aluminium GdBa2Cu3O7 (Janossy et al. 1997)

  27. Selected experimental results (ctd.) B. Quasiparticle spin susceptibility 3He-A, B (Ahonen et al., 1976) 3He-A , 3He-B

  28. Selected experimental results (ctd.) C. Magnetic field penetration depth Mercury UBe13 F. Gross et al., WMI, 1985

  29. Selected experimental results (ctd.) C. Magnetic field penetration depth UPt3 (S. Schöttl et al., WMI, 1999) YBa2Cu3O7 (W. Hardy et al., 1994)

  30. Selected experimental results (ctd.) D. Electronic Raman scattering Bi 2212 (Hackl et al., WMI, 1994) Nb3Sn (Hackl et al., 1989)

  31. Summary and conclusion: superconductivity and superfluidity Physics Nobel prize 2003 Overwhelming application spectrum of the work by Vitalii Ginzburg, Alexei Abrikosov und Tony Leggett Normal state of pair-correlated Fermi systems Momentum relaxation and Drude conductivity Momentum conservation, shear viscosity and Hagen-Poiseuille law Generalized BCS model of superconductivity and superfluidity Parabolic Bands in D=3 und D=2 Weak coupling limit Model pairing states Superfluid 3He First unconventional BCS superfluid (p-wave triplet pairing) Quantitative results for response und transport properties Implications for unconventional metallic superconductors Unconventional superconductors Singlet d-wave vs. triplet p- or f-wave Nodal quasiparticles and low temperature power laws Application to Heavy Fermion SC‘s, organic SC‘s, Cuprates, Sr2RuO4

  32. Future prospects: superconductivity and superfluidity Unconventional superconductivity, pairing symmetries, mechanisms, transport prop‘s. Electron-doped cuprates Hole-doped cuprates: full doping dependence Heavy Fermion SC‘s: UPt3, UBe13, ... Organic superconductors The Ruddlesden-Popper system Sr2Ru04 Dirty Fermi superfluids: 3He in aerogel Local Response Transport and Relaxation Zero Sound Spin waves Multiple spin echos Pair vibration modes Two-fluid description of pair-correlated Fermi systems Transport properties Thermoelectric/mechanic effects Analytic treatment of the quasiparticle response and transport

  33. Appendix A: Matthiessen rule classification transport in metals transport in clean Fermi liquids transport in dirty Fermi liquids (3He in aerogel) momentum relaxation (elastic) momentum relaxation (el. + inel.) momentum conservation

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