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Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für...

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

    Dietrich EinzelWalther-Meiner-Institut fr TieftemperaturforschungBayerische Akademie der Wissenschaften


    Phenomenological description Superconducting and superfluid systems Generalized microscopic description* D. Einzel, Lexikon der Physik, Spektrum Akademischer Verlag, Heidelberg, 2000

  • Motivation: Physics Nobel prize 2003Alexei A. Abrikosov (born 1928)Argonne National Laboratory,USAVitalii L. Ginzburg (born 1916)P. N. Lebedev Physical InstituteMoscowAnthony J. Leggett (born 1938) University of Illinois atUrbana-Champaign, USA

  • Phenomenological description: London vs. Ginzburg-LandauQM particle with mass M, charge Q, density Ns in external el.mag. PotentialsQuantum-mechanical condensate wave functionF. und H. London, 1935, Max von Laue, 1938, V. L. Ginzburg und L. L. Landau, 1950Schrdinger equationcharge-supercurrentNeutral masssupercurrentApplication: pairs

  • Merits of the London theoryPersistent currentsMagnetic field screeningFluxoid quantisationJosephson effectsGauge invarianceThe London theory does not explain:Q=2e Microscopic origin of NsNon-local effectsFlux linesInterfacesGinzburg-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:All London resultsNon-local effectsDistinction: type-I and type-IIFlux line lattice Arbitrary boundary conditionsThousands of citationsQ=2e Microscopic origin of NsBehavior at lower temperatures T
  • Superconducting and superfluid systems

  • Superconducting and superfluid systems (ctd.)

  • Current relaxation in normal Fermi liquidsCharged Fermions in metalsNeutral Fermi liquidsDrudeslawHagen-Poiseuilleslawmomentum conservation(exception: walls)momentum relaxation:impurities, Phonons...

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

  • GUT of superconductivity and superfluidity charged neutral

    Fermi Bose

    spin singlet spin triplet even parity odd parity

    BCS non-BCS

    conventionel unconventionelAspects andsystems to be unified:Restrictions: pair correlated Fermi systems

    weak coupling limit

    parabolic bands in D=3 und D=2

  • BCS mean field treatment of superconductivity and superfluidityPair attraction nearthe Fermi surfaceSpontaneous pair formation in k-space: pair (Gorkov-) amplitude Pair potential (energy gap)Broken gaugesymmetry

  • Classification of pair potentialsA. Spin structure Pauli principle:Singlet (s=0): even parityTriplet (s=1): odd parity

  • Classification of pair potentials (ctd.)B. Orbital structure Conventional pairingshares the symmetry of the Fermi surface;only gauge symmetry brokenExamples: classical singlet SCs like Hg, Al, V, ...

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

  • Conventional and unconventional model pairing states:S=0: singletS=1: triplet

    System NameNode-structure conv. SCs 1 - isotropic 3He-A UBe13Axial (3D)

    3He-B - pseudo- isotropic UPt13 - E1g

    E2u Cuprates (hole- doped) - B1g Sr2RuO4Axial (2d)B1g x Eu

  • The d-wave controversy in the High-Tc communityPHYSICS TODAY MAY 1993





  • 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 spaceNota bene: spontaneous pair formation

    off-diagonal long range order (ODLRO)

  • Bogoliubov-Valatin- diagonalisation Excitation spectrum ofBogoliubov-quasiparticlesQuasiparticle HamiltonianMomentum distributionof Bogoliubov-quasiparticles0n(xp)n(Ep)x/kT

  • Linear response of the quasiparticle systemExternal perturbationsThermal excitationsin local equilibriumtemperature changemagnetic fieldvector potentialThermally activated vs. nodal quasiparticlesAmpereZeemantemperature

  • Linear response of the condensate (BCS-Leggett theory)MacroscopiclimitBroken gaugesymmetryBroken spin-orbit symmetry(SBSOS)Leggett, 1971Charge supercurrentNew: spin supercurrent

  • 01201T/TcisotropicaxialB1g, E1g,E2uC(T)/CN(T)Heat capacity ofBogoliubov-quasiparticles

  • Spin susceptibilityof Bogoliubov-quasiparticles10

  • 0101T/TcisotropicE1g(||)E2uB1gE1g( )Bogoliubov quasiparticlecurrent and magneticfield penetration depthdlLm(T)/lLm(0)

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

  • Selected experimental resultsA. Quasiparticle heat capacity

    Vanadium and Tin

    UBe13 (H.-R. Ott et al., 1983)

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

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


  • Selected experimental results (ctd.)B. Quasiparticle spin susceptibility 3He-A, B(Ahonen et al., 1976)3He-A3He-B,

  • Selected experimental results (ctd.)C. Magnetic field penetration depth


    UBe13F. Gross et al., WMI, 1985

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

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

  • Summary and conclusion: superconductivity and superfluidityPhysics 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 conductivityMomentum conservation, shear viscosity and Hagen-Poiseuille law

    Generalized BCS model of superconductivity and superfluidity

    Parabolic Bands in D=3 und D=2Weak coupling limit Model pairing states

    Superfluid 3He

    First unconventional BCS superfluid (p-wave triplet pairing)Quantitative results for response und transport propertiesImplications for unconventional metallic superconductors

    Unconventional superconductors

    Singlet d-wave vs. triplet p- or f-waveNodal quasiparticles and low temperature power lawsApplication to Heavy Fermion SCs, organic SCs, Cuprates, Sr2RuO4

  • Future prospects: superconductivity and superfluidityUnconventional superconductivity, pairing symmetries, mechanisms, transport props.

    Electron-doped cuprates Hole-doped cuprates: full doping dependenceHeavy Fermion SCs: UPt3, UBe13, ...Organic superconductorsThe Ruddlesden-Popper system Sr2Ru04

    Dirty Fermi superfluids: 3He in aerogel

    Local ResponseTransport and RelaxationZero SoundSpin wavesMultiple spin echosPair vibration modes

    Two-fluid description of pair-correlated Fermi systems

    Transport propertiesThermoelectric/mechanic effectsAnalytic treatment of the quasiparticle response and transport

  • Appendix A: Matthiessen rule classification

    transport in metals

    transport in cleanFermi liquids

    transport in dirtyFermi liquids(3He in aerogel)

    momentum conservation

    momentum relaxation(el. + inel.)momentumrelaxation(elastic)