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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
* D. Einzel, Lexikon der Physik, Spektrum Akademischer Verlag, Heidelberg, 2000
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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
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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
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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
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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
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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 -
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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...
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Indications of superconductivity:Vanishing resistance Heike Kamerlingh-Onnes, 1911
Indications of superfluidity:Vanishing shear viscosity (?)J. M. Parpia, D. Einzel., 1987
viscosity paradox
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„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
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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
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Classification of pair potentials
A. Spin structure
Pauli principle:
Singlet (s=0): even parity
Triplet (s=1): odd parity
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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
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(Moritz, 11 years)
The broken lattice symmetry in cuprates
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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
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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
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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)
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Bogoliubov-Valatin- diagonalisation
Excitation spectrum ofBogoliubov-quasiparticles
Quasiparticle Hamiltonian
Momentum distributionof Bogoliubov-quasiparticles
0
np
(Ep)
/kT
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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
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Linear response of the condensate (BCS-Leggett theory)
Macroscopiclimit
Broken gaugesymmetry
Broken spin-orbit symmetry(SBSOS)Leggett, 1971
Charge supercurrent
New: spin supercurrent
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0 1
2
0
1
T/Tc
isotropic
axial
B1g, E1g,
E2u
C(T)/CN(T)Heat capacity ofBogoliubov-quasiparticles
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Spin susceptibilityof Bogoliubov-quasiparticles
1
0
0 1T/Tc
axial
pseudoisotropic
B1g, E1g
E2u
isotropic
(T)/N
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0
1
0
1T/Tc
isotropic
E1g(||)
E2u
B1g
E1g( )
Bogoliubov quasiparticlecurrent and magneticfield penetration depth
L(T)/L(0)
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The unconventional superconductivity in UPt3 (J. A. Sauls et al., 1996)
singlet even parity (E1g) triplet odd parity (E2u)
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Selected experimental results
A. Quasiparticle heat capacity
Vanadium and Tin UBe13 (H.-R. Ott et al., 1983)
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Selected experimental results (ctd.)
YBa2Cu3O7
(Junod et al., 1996) Sr2RuO4
(Deguchi et al., 2000)
A. Quasiparticle heat capacity
T[K]
C(T)/CN(T)
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Selected experimental results (ctd.)
B. Quasiparticle spin susceptibility
GdBa2Cu3O7 (Janossy et al. 1997)
Aluminium
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Selected experimental results (ctd.)
B. Quasiparticle spin susceptibility
3He-A, B(Ahonen et al., 1976)
3He-A
3He-B
,
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Selected experimental results (ctd.)
C. Magnetic field penetration depth
Mercury UBe13
F. Gross et al., WMI, 1985
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Selected experimental results (ctd.)
C. Magnetic field penetration depth
UPt3 (S. Schöttl et al., WMI, 1999)
YBa2Cu3O7
(W. Hardy et al., 1994)
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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
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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
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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
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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)