Superconductivity and Superfluidity *

Dietrich EinzelWalther-Meiner-Institut fr TieftemperaturforschungBayerische Akademie der Wissenschaften

Outlook:

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

IN HIGH-TC SUPERCONDUCTORS,IS d-WAVE THE NEW WAVE?

BARBARA GOSS-LEVIPHYSICS TODAYPHYSICS TODAY FEBRUARY 1994

IN EXPLAINING HIGH-TC,IS d-WAVE A WASHOUT?

PHILIP W. ANDERSONPRINCETON UNIVERSITY

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)

Aluminium

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

Mercury

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)