Theory of Fluctuations in Superconductors 1st Edition by Anatoly Larkin, Andrei Varlamov ISBN 978-0199564835 0199564833
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ISBN 10: 0199564833
ISBN 13: 978-0199564835
Author: Anatoly Larkin, Andrei Varlamov
This book presents a complete encyclopaedia of superconducting fluctuations, summarising the last thirty-five years of work in the field. The first part of the book is devoted to an extended discussion of the Ginzburg-Landau phenomenology of fluctuations in its thermodynamical and time-dependent versions and its various applications. The second part deals with microscopic justification of the Ginzburg-Landau approach and presents the diagrammatic theory of fluctuations. The third part is devoted to a less-detailed review of the manifestation of fluctuations in observables: diamagnetism, magnetoconductivity, various tunneling characteristics, thermoelectricity, and NMR relaxation. The final chapters turn to the manifestation of fluctuations in unconventional superconducting systems: nanodrops, nanorings, Berezinsky-Kosterlitz-Thouless state, quantum phase transition between superconductor and insulator, and thermal and quantum fluctuations in weak superconducting systems. The book ends with a brief discussion on theories of high temperature superconductivity, where fluctuations appear as the possible protagonist of this exciting phenomenon.
Table of contents:
I PHENOMENOLOGY OF FLUCTUATIONS: GINZBURG-LANDAU FORMALISM
1 Introduction
2 Fluctuation thermodynamics
2.1 Ginzburg-Landau theory
2.1.1 GL functional
2.1.2 Heat capacity jump
2.1.3 GL equations
2.2 Fluctuation contribution to heat capacity
2.2.1 Zero dimensionality: the exact solution
2.2.2 Arbitrary dimensionality: case T > Tc.
2.2.3 Arbitrary dimensionality: case T < Tc.
2.3 Fluctuation diamagnetism
2.3.1 Qualitative preliminaries
2.3.2 Zero-dimensional diamagnetic susceptibility
2.3.3 2D magnetization
2.4 Layered superconductor in magnetic field
2.4.1 Lawrence-Doniach model
2.4.2 General formula for the fluctuation free energy in magnetic field
2.4.3 Fluctuation magnetization and its crossovers
2.4.4 Fluctuation heat capacity in magnetic field
2.5 Ginzburg-Levanyuk criterion
2.5.1 Definition of the Gi number from the heat capacity in zero magnetic field
2.5.2 Other definitions
2.5.3 Broadening of the critical region by a magnetic field
2.6 Scaling and the renormalization group
2.7 Effect of fluctuations on superfluid density and critical temperature
2.8 Fluctuations of magnetic field
3 Fluctuation transport
3.1 Time-dependent GL equation
3.2 General expression for paraconductivity
3.3 Paraconductivity of a layered superconductor
3.3.1 In-plane conductivity
3.3.2 Out-of plane conductivity
3.3.3 Analysis of the limiting cases
3.4 Hall paraconductivity
3.5 Magnetic field angular dependence of paraconductivity
3.6 Paraconductivity of nanotubes
3.6.1 Paraconductivity in zero magnetic field
3.6.2 Fluctuation magnetoconductivity
3.6.3 Discussion
3.7 Transport equation for fluctuation Cooper pairs
4 Fluctuations in vortex structures
4.1 Vortex lattice and magnetic flux resistivity
4.2 Collective pinning
4.2.1 Correlation length
4.2.2 Critical current
4.2.3 Collective pinning in other systems
4.2.4 Thermal depinning
4.3 Creep
4.4 Melting of the vortex lattice
II BASIC NOTIONS OF THE MICROSCOPIC THEORY
5 Microscopic derivation of the TDGL equation
5.1 Preliminaries
5.2 The Cooper channel of electron-electron interaction: the fluctuation propagator
5.3 Diagrammatic representation of fluctuation corrections
5.4 Superconductor with impurities
5.4.1 Accounting for electron scattering by impurities
5.4.2 Propagator for superconductor with impurities
5.5 Layered superconductor
6 Microscopic derivation of the GL functional
6.1 GL functional of a conventional superconductor
6.2 GL functional in the case of a nontrivial order parameter symmetry
7 Microscopic theory of fluctuation conductivity
7.1 Qualitative discussion of the different fluctuation contributions
7.2 The electromagnetic response operator
7.3 Fluctuation conductivity of a layered superconductor in the vicinity of Te
7.3.1 AL contribution
7.3.2 Contributions from fluctuations of the DOS
7.3.3 MT contribution
7.3.4 Phase-breaking time T
7.3.5 Comparison with the experiment
7.4 Fluctuation conductivity in a.c. field
7.5 Fluctuation conductivity in ultra-clean superconductors
7.5.1 Preliminaries
7.5.2 Nonlocal fluctuation conductivity in quasi-ballistic regime
7.5.3 Discussion
7.6 Fluctuation conductivity far from Te
7.6.1 Paraconductivity of clean superconductor for T> Tc
7.6.2 Fluctuation conductivity of impure superconductor for T > T
7.6.3 The effect of inter-electron interaction in Cooper channel on the conductivity of disordered metal
7.7 Nonlinear fluctuation effects
III MANIFESTATION OF FLUCTUATIONS IN OBSERVABLES
8 Fluctuations in magnetic field
8.1 Magnetoconductivity in the vicinity of transition
8.1.1 Self-consistent treatment of the critical temperature shift in magnetic field
8.2 Magnetoconductivity far from transition
8.3 Effect of fluctuations on the Hall conductivity
8.3.1 AL contribution to the Hall conductivity
8.3.2 Effect of topological singularity on fluctuation Hall effect
8.4 Fluctuation magnetic susceptibility far from transition
8.5 Fluctuations in magnetic fields above Hc2(0)
8.5.1 Conductivity
8.5.2 Magnetization
9 DOS and tunneling
9.1 Density of states of superconductor in fluctuation regime
9.2 Fluctuation phenomena in tunnel junction above Te
9.2.1 Preliminaries
9.2.2 The effect of fluctuations on the tunnel current above Te
9.3 Fluctuation phenomena in N(S)-I-S junction
9.3.1 Quasiparticle current in N(S)-I-S junction
9.3.2 Effective boundary Hamiltonian
9.3.3 General formula for normal tunneling current
9.3.4 Andreev conductance
9.3.5 Pair-field susceptibility of a superconductor
9.3.6 Goldman’s group experiments
9.4 Fluctuation tunneling anomaly in a superconductor above the paramagnetic limit
9.5 The magnetoresistance of a granular superconducting metal
9.5.1 Choice of the model
9.5.2 Cooperon and propagator for granular superconductor
9.5.3 Suppression of the conductivity due to DOS fluctuations
9.5.4 Zeeman splitting
9.5.5 Conclusions
10 Effect of fluctuations on thermoelectricity and heat transport
10.1 Equations of heat and electric transfer
10.2 Phenomenological definition of the heat current
10.3 Heat current operator for interacting electrons
10.4 Fluctuation thermoelectric power above the superconducting transition
10.4.1 Generalities
10.4.2 Effect of the DOS fluctuations
10.4.3 AL contribution to the thermoelectric power
10.4.4 Discussion
10.5 Thermal conductivity
10.6 Manifestation of superconducting fluctuations in the Nernst effect
11 Spin susceptibility and NMR
11.1 Preliminaries
11.2 Spin susceptibility
11.3 Relaxation rate
11.4 Discussion
IV FLUCTUATIONS IN NANOSTRUCTURES AND UNCONVENTIONAL SUPERCONDUCTING SYSTEMS
12 Fluctuations in nanograins, nanodrops and granular superconductors
12.1 Ultrasmall superconducting grains
12.2 Superconducting drops in system with quenched disorder
12.2.1 The optimal fluctuations in the vicinity of Te
12.2.2 Formation of the superconducting drops in magnetic fields H > He2 (0)
12.3 Exponential DOS tail in superconductor with quenched disorder
12.4 Josephson coupled superconducting grains and drops
12.5 Classical phase transition in granular superconductors
12.5.1 XY-model for granular superconductor
12.5.2 GL description of the granular superconductor
12.5.3 The broadening of superconducting transition by the quenched disorder
12.6 Quantum phase transition in granular superconductors
12.6.1 Coulomb suppression of superconductivity in the array of tunnel coupled granules
12.6.2 Superconducting grains in the normal metal matrix
12.6.3 Phase transition in disordered superconducting film in strong magnetic field
13 Fluctuations in Josephson junctions
13.1 General properties of a Josephson junction
13.1.1 Stationary Josephson effect
13.1.2 Nonstationary Josephson effect
13.2 Fluctuation broadening of the emission line
13.2.1 Thermal fluctuations of the voltage
13.2.2 Thermal fluctuations of the order parameter
13.3 Fluctuation suppression of the Josephson current below Te
13.4 Josephson current decay due to the thermal phase fluctuations
13.5 Macroscopic quantum tunneling
13.5.1 Pair tunneling in the case of zero viscosity
13.5.2 Case of low viscosity: Q≫ 1
13.5.3 Case of high viscosity: Q1
14 Phase slip events
14.1 Classical phase-slip events
14.2 Quantum phase slip events in nanorings
15 Phase fluctuations in a 2D superconducting system
15.1 The crucial role of phase fluctuations in 2D systems
15.2 Exponential tail in the Josephson current close to Te
15.3 Berezinskii-Kosterlitz-Thouless transition
15.4 Manifestation of vortex fluctuations above BKT transition
16 Fluctuations near superconductor-insulator transition
16.1 Quantum phase transition
16.2 3D case
16.3 2D superconductors
16.3.1 Preliminaries
16.3.2 Boson mechanism of Te suppression
16.3.3 Fermion mechanism of Te suppression
17 Role of fluctuations in high temperature superconductivity
17.1 Phase diagram
17.2 Resonating valence bond theory
17.2.1 Strongly correlated Fermi systems
17.2.2 Spin-charge separation
17.2.3 Hidden order phase
17.3 Bose-metal
17.3.1 Staggered flux state
17.3.2 Vortices localization
17.3.3 Bipolarons
17.4 BCS scenarios
17.4.1 Strong coupling BCS-like schemes
17.4.2 BEC-BCS scenario
17.5 Phenomenology
17.5.1 Marginal Fermi liquid
17.5.2 Bose phenomenology
A Relations between parameters of micro- and macroscopic theories
A.1 Coherence length
A.2 Other GL functional parameters
B Properties of the Euler gamma function and its logarithmic derivatives
B.1 Euler gamma function
B.2 Digamma function and its derivatives
C Integrals of the Lawrence-Doniach theory
References
Glossary
Index
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Tags: Anatoly Larkin, Andrei Varlamov, Theory of Fluctuations