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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
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Page 1: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

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

Page 2: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Motivation: Physics Nobel prize 2003

Alexei A. Abrikosov (born 1928)Argonne National Laboratory,USA

Vitalii L. Ginzburg (born 1916)P. N. Lebedev Physical InstituteMoscow

Anthony J. Leggett (born 1938) University of Illinois atUrbana-Champaign, USA

Page 3: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Phenomenological description: London vs. Ginzburg-Landau

QM particle with mass M, charge Q, density Ns in external el.mag. Potentials

Quantum-mechanical condensate wave functionF. und H. London, 1935, Max von Laue, 1938, V. L. Ginzburg und L. L. Landau, 1950

Schrödinger equation

charge-supercurrent

Neutral masssupercurrent

Application: pairs

Page 4: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Merits of the London theory

Persistent currentsMagnetic field screeningFluxoid quantisationJosephson effectsGauge invariance

The London theory does not explain:

Q=2e Microscopic origin of Ns

Non-local effectsFlux linesInterfaces

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:

All London resultsNon-local effectsDistinction: type-I and type-IIFlux line lattice Arbitrary boundary conditionsThousands of citations

Q=2e Microscopic origin of Ns

Behavior at lower temperatures T<<Tc

Page 5: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Superconducting and superfluid systems

System Fermi/Bose SC/SF Tc[K] Discovery Nobel prize

Hg Fermi SC 4.2 1911 1913

Liquid 4He BoseSF 2.17 1924 - 1938 1978

A15

compoundsFermi SC 20 1954, 1973 -

Pulsars Fermi SF 108 1968 -

Liquid 3HeFermi SF 10-3 1971 1996

Page 6: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Superconducting and superfluid systems (ctd.)

System Fermi/Bose SC/SF Tc[K] Discovery Nobel prize

Heavy

Fermions Fermi SC 1 1979 -

Organic

SC‘sFermi SC 10 1979 -

Cuprates Fermi SC 100 1986 1987

Sr2RuO4 Fermi SC 1 1993 -

Molecular

HydrogenBose SF 0.2 2000 -

Page 7: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Current relaxation in normal Fermi liquids

Charged Fermions in metals

Neutral Fermi liquids

Drude‘slaw

Hagen-Poiseuille‘s

law momentum conservation(exception: walls)

momentum relaxation:impurities, Phonons...

Page 8: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Indications of superconductivity:Vanishing resistance Heike Kamerlingh-Onnes, 1911

Indications of superfluidity:Vanishing shear viscosity (?)J. M. Parpia, D. Einzel., 1987

viscosity paradox

Page 9: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

„GUT“ of superconductivity and superfluidity

charged neutral

Fermi Bose

spin singlet spin triplet even parity odd parity

BCS „non-BCS“

conventionel unconventionel

Aspects andsystems to be unified:

Restrictions:

pair correlated Fermi systems

weak coupling limit

parabolic bands in D=3 und D=2

Page 10: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

BCS mean field treatment of superconductivity and superfluidity

Pair attraction nearthe Fermi surface

Spontaneous pair formation in k-space: pair (Gor‘kov-) amplitude

Pair potential (energy gap)

Broken gaugesymmetry

Page 11: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Classification of pair potentials

A. Spin structure

Pauli principle:

Singlet (s=0): even parity

Triplet (s=1): odd parity

Page 12: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

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, ...

Unconventional pairing

has lower symmetry as the Fermi surface;additional broken symmetries

Examples: see next slide

Page 13: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

(Moritz, 11 years)

The broken lattice symmetry in cuprates

Page 14: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Conventional and unconventional

model pairing states:

System NameNode-

structure

conv.

SC‘s 1 - isotropic

3He-A

UBe13

Axial (3D)

3He-B -

pseudo-

isotropic

UPt13

- E1g

E2u

Cuprates

(hole-

doped)

-

B1g

Sr2RuO4

Axial (2d)

B1g x Eu

S=0: singletS=1: triplet

Page 15: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

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-LEVIPHYSICS TODAY

PHYSICS TODAY FEBRUARY 1994

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

PHILIP W. ANDERSONPRINCETON UNIVERSITY

Page 16: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

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)

Page 17: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Bogoliubov-Valatin- diagonalisation

Excitation spectrum ofBogoliubov-quasiparticles

Quasiparticle Hamiltonian

Momentum distributionof Bogoliubov-quasiparticles

0

np

(Ep)

/kT

Page 18: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Linear response of the quasiparticle system

External perturbations

Thermal excitationsin local equilibrium

temperature change

magnetic field

vector potential

Thermally activated vs. nodal quasiparticles

Ampere Zeeman

temperature

Page 19: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Linear response of the condensate (BCS-Leggett theory)

Macroscopiclimit

Broken gaugesymmetry

Broken spin-orbit symmetry(SBSOS)Leggett, 1971

Charge supercurrent

New: spin supercurrent

Page 20: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

0 1

2

0

1

T/Tc

isotropic

axial

B1g, E1g,

E2u

C(T)/CN(T)Heat capacity ofBogoliubov-quasiparticles

Page 21: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Spin susceptibilityof Bogoliubov-quasiparticles

1

0

0 1T/Tc

axial

pseudoisotropic

B1g, E1g

E2u

isotropic

(T)/N

Page 22: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

0

1

0

1T/Tc

isotropic

E1g(||)

E2u

B1g

E1g( )

Bogoliubov quasiparticlecurrent and magneticfield penetration depth

L(T)/L(0)

Page 23: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

The unconventional superconductivity in UPt3 (J. A. Sauls et al., 1996)

singlet even parity (E1g) triplet odd parity (E2u)

Page 24: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Selected experimental results

A. Quasiparticle heat capacity

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

Page 25: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Selected experimental results (ctd.)

YBa2Cu3O7

(Junod et al., 1996) Sr2RuO4

(Deguchi et al., 2000)

A. Quasiparticle heat capacity

T[K]

C(T)/CN(T)

Page 26: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Selected experimental results (ctd.)

B. Quasiparticle spin susceptibility

GdBa2Cu3O7 (Janossy et al. 1997)

Aluminium

Page 27: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Selected experimental results (ctd.)

B. Quasiparticle spin susceptibility

3He-A, B(Ahonen et al., 1976)

3He-A

3He-B

,

Page 28: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Selected experimental results (ctd.)

C. Magnetic field penetration depth

Mercury UBe13

F. Gross et al., WMI, 1985

Page 29: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Selected experimental results (ctd.)

C. Magnetic field penetration depth

UPt3 (S. Schöttl et al., WMI, 1999)

YBa2Cu3O7

(W. Hardy et al., 1994)

Page 30: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Selected experimental results (ctd.)

D. Electronic Raman scattering

Bi 2212 (Hackl et al., WMI, 1994)

Nb3Sn (Hackl et al., 1989)

Conventional

superconductors

0

1

2

3

E g

Inte

nsi

ty (cp

s/m

W)

Raman shift (cm )w - 1

0 50 100

6 K

19 K

Nb Sn

T = 18 K3

c

Hackl et al., Physica C , 431 (1989)162-164

Cuprate

superconductors

0

2

4

6

8

10Bi- 2212T = 86 Kc

0 200 400 600Raman shift (cm )w - 1

20 K

A1g

B1g

B2gIn

tensi

ty (cp

s/m

W)

Devereaux et al., PRL , 3291 (1994)72

Page 31: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

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 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 SC‘s, organic SC‘s, Cuprates, Sr2RuO4

Page 32: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

Future prospects: superconductivity and superfluidity

Unconventional superconductivity, pairing symmetries, mechanisms, transport prop‘s.

Electron-doped cuprates Hole-doped cuprates: full doping dependenceHeavy Fermion SC‘s: 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

Page 33: Superconductivity and Superfluidity * Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften Outlook:

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)


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