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