Theory of fluctuations in superconductors:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
2005
|
| Series: | International series of monographs on physics
127 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 412 S. graph. Darst. |
| ISBN: | 0198528159 9780198528159 |
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| 245 | 1 | 0 | |a Theory of fluctuations in superconductors |c Anatoly Larkin and Andrei Varlamov |
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| _version_ | 1804133240197349376 |
|---|---|
| adam_text | CONTENTS
I PHENOMENOLOGY OF FLUCTUATIONS: GINZBURG
LANDAU FORMALISM
1
Introduction
3
2
Fluctuation thermodynamics
7
2.1
Ginzburg-Landau theory
7
2.1.1
GL functional
7
2.1.2
Heat capacity jump
9
2.1.3
GL equations
9
2.2
Fluctuation contribution to heat capacity
12
2.2.1
Zero dimensionality: the exact solution
12
2.2.2
Arbitrary dimensionality: case
Τ
>
Тс. ІЗ
2.2.3
Arbitrary dimensionality: case
Τ
<
Tc.
15
2.3
Fluctuation diamagnetism
16
2.3.1
Qualitative preliminaries
16
2.3.2
Zero-dimensional diamagnetic susceptibility
19
2.3.3
2D magnetization
21
2.4
Layered superconductor in magnetic field
25
2.4.1
Lawrence-Doniach model
25
2.4.2
General formula for the fluctuation free energy
in magnetic field
27
2.4.3
Fluctuation magnetization and its crossovers
28
2.4.4
Fluctuation heat capacity in magnetic field
31
2.5
Ginzburg-Levanyuk criterion
31
2.5.1
Definition of the Gi number from the heat capacity
in zero magnetic field
31
2.5.2
Other definitions
33
2.5.3
Broadening of the critical region by a magnetic
field
34
2.6
Scaling and the renormalization group
37
2.7
Effect of fluctuations on superfluid density and critical
temperature
45
2.8
Fluctuations of magnetic field
50
3
Fluctuation transport
52
3.1
Time-dependent GL equation
52
3.2
General expression for paraconductivity
54
3.3
Paraconductivity of a layered superconductor
57
3.3.1
In-plane conductivity
58
vu
CONTENTS
3.3.2 Out-of plane
conductivity
59
3.3.3
Analysis of the limiting cases
60
3.4
Hall paraconductivity
62
3.5
Magnetic field angular dependence
of paraconductivity
65
3.6
Paraconductivity of nanotubes
69
3.6.1
Paraconductivity in zero magnetic field
71
3.6.2
Fluctuation magnetoconductivity
72
3.6.3
Discussion
73
3.7
Transport equation for fluctuation Cooper pairs
74
Fluctuations in vortex structures
78
4.1
Vortex lattice and magnetic flux resistivity
78
4.2
Collective pinning
80
4.2.1
Correlation length
81
4.2.2
Critical current
83
4.2.3
Collective pinning in other systems
84
4.2.4
Thermal depinning
84
4.3
Creep
85
4.4
Melting of the vortex lattice
89
II BASIC NOTIONS OF THE MICROSCOPIC THEORY
Microscopic derivation of the TDGL equation
95
5.1
Preliminaries
95
5.2
The Cooper channel of electron-electron interaction:
the fluctuation propagator
96
5.3
Diagrammatic representation of fluctuation corrections
100
5.4
Superconductor with impurities
102
5.4.1
Accounting for electron scattering by impurities
102
5.4.2
Propagator for superconductor with impurities
104
5.5
Layered superconductor
107
Microscopic derivation of the GL functional
109
6.1
GL functional of a conventional superconductor
109
6.2
GL functional in the case of
a
nontrivial
order
parameter symmetry
114
Microscopic theory of fluctuation conductivity
118
7.1
Qualitative discussion of the different fluctuation
contributions
118
7.2
The electromagnetic response operator
120
7.3
Fluctuation conductivity of a layered superconductor
in the vicinity of Tc
122
7.3.1
AL
contribution
122
7.3.2
Contributions from fluctuations of the DOS
126
CONTENTS
7.3.3
MT
contribution
131
7.3.4
Phase-breaking time
τφ
138
7.3.5
Comparison with the experiment
142
7.4
Fluctuation conductivity in a.c. field
146
7.5
Fluctuation conductivity in ultra-clean
superconductors
148
7.5.1
Preliminaries
148
7.5.2
Nonlocal fluctuation conductivity in quasi-ballistic
regime
150
7.5.3
Discussion
156
7.6
Fluctuation conductivity far from Tc
157
7.6.1
Paraconductivity of clean superconductor for
Τ
»
Tc
157
7.6.2
Fluctuation conductivity of impure superconductor
for T^TC
160
7.6.3
The effect of inter-electron interaction in Cooper
channel on the conductivity of disordered metal
174
7.7
Nonlinear fluctuation effects
179
III MANIFESTATION OF FLUCTUATIONS
IN
OBSERVABLES
8
Fluctuations in magnetic field
185
8.1
Magnetoconductivity in the vicinity of transition
185
8.1.1
Self-consistent treatment of the critical
temperature shift in magnetic field
190
8.2
Magnetoconductivity far from transition
192
8.3
Effect of fluctuations on the Hall conductivity
195
8.3.1
AL
contribution to the Hall conductivity
195
8.3.2
Effect of topological singularity on fluctuation
Hall effect
197
8.4
Fluctuation magnetic susceptibility far from transition
201
8.5
Fluctuations in magnetic fields above i/C2(0)
203
8.5.1
Conductivity
203
8.5.2
Magnetization
207
9
DOS and tunneling
211
9.1
Density of states of superconductor in fluctuation
regime
211
9.2
Fluctuation phenomena in tunnel junction above Tc
213
9.2.1
Preliminaries
213
9.2.2
The effect of fluctuations on the tunnel current
above Tc
217
9.3
Fluctuation phenomena in N(S)-I-S junction
220
9.3.1
Quasiparticle current in N(S)-I-S junction
221
CONTENTS
9.3.2
Effective boundary Hamiltonian
221
9.3.3
General formula for normal tunneling current
224
9.3.4
Andreev conductance
225
9.3.5
Pair-field susceptibility of a superconductor
226
9.3.6
Goldman s group experiments
227
9.4
Fluctuation tunneling anomaly in a superconductor
above the paramagnetic limit
232
9.5
The magnetoresistance of a granular superconducting
metal
238
9.5.1
Choice of the model
240
9.5.2
Cooperon and propagator for granular
superconductor
241
9.5.3
Suppression of the conductivity due to DOS
fluctuations
245
9.5.4
Zeeman
splitting
248
9.5.5
Conclusions
250
10
Effect of fluctuations on thermoelectricity and heat
transport
252
10.1
Equations of heat and electric transfer
252
10.2
Phenomenological definition of the heat current
253
10.3
Heat current operator for interacting electrons
254
10.4
Fluctuation thermoelectric power above the
superconducting transition
256
10.4.1
Generalities
256
10.4.2
Effect of the DOS fluctuations
257
10.4.3
AL
contribution to the thermoelectric power
259
10.4.4
Discussion
260
10.5
Thermal conductivity
261
10.6
Manifestation of superconducting fluctuations in the
Nernst effect
263
11
Spin susceptibility and NMR
266
11.1
Preliminaries
266
11.2
Spin susceptibility
267
11.3
Relaxation rate
268
11.4
Discussion
270
IV FLUCTUATIONS IN NANOSTRUCTURES AND
UNCONVENTIONAL SUPERCONDUCTING SYSTEMS
12
Fluctuations in nanograins, nanodrops and granular
superconductors
273
12.1 Ultrasmali
superconducting grains
273
CONTENTS
12.2 Superconducting
drops in system with quenched
disorder
277
12.2.1
The optimal fluctuations in the vicinity of Tc
277
12.2.2
Formation of the superconducting drops in
magnetic fields
H
>
Hc2
(0) 279
12.3
Exponential DOS tail in superconductor with quenched
disorder
283
12.4
Josephson
coupled superconducting grains and drops
285
12.5
Classical phase transition in granular superconductors
287
12.5.1
ХУ
-model
for granular superconductor
287
12.5.2
GL description of the granular superconductor
287
12.5.3
The broadening of superconducting transition
by the quenched disorder
288
12.6
Quantum phase transition in granular superconductors
291
12.6.1
Coulomb suppression of superconductivity in the
array of tunnel coupled granules
291
12.6.2
Superconducting grains in the normal metal
matrix
292
12.6.3
Phase transition in disordered superconducting
film in strong magnetic field
295
13
Fluctuations in
Josephson
junctions
299
13.1
General properties of
a Josephson
junction
299
13.1.1
Stationary
Josephson
effect
299
13.1.2
Nonstationary
Josephson
effect
303
13.2
Fluctuation broadening of the emission line
304
13.2.1
Thermal fluctuations of the voltage
304
13.2.2
Thermal fluctuations of the order parameter
308
13.3
Fluctuation suppression of the
Josephson
current
below Tc
310
13.4
Josephson
current decay due to the thermal phase
fluctuations
313
13.5
Macroscopic quantum tunneling
317
13.5.1
Pair tunneling in the case of zero viscosity
319
13.5.2
Case of low viscosity:
Q
» 1 321
13.5.3
Case of high viscosity:
Q
< 1 322
14
Phase slip events
325
14.1
Classical phase-slip events
325
14.2
Quantum phase slip events in nanorings
327
15
Phase fluctuations in a 2D superconducting system
335
15.1
The crucial role of phase fluctuations in 2D systems
335
15.2
Exponential tail in the
Josephson
current close to Tc
336
15.3
Berezinskii-Kosterlitz-Thouless transition
338
CONTENTS
15.4 Manifestation
of vortex fluctuations above BKT
transition
341
16
Fluctuations near superconductor-insulator
transition
343
16.1
Quantum phase transition
343
16.2 3D
case
344
16.3
2D superconductors
348
16.3.1
Preliminaries
348
16.3.2
Boson mechanism of Tc suppression
349
16.3.3
Fermion mechanism of Tc suppression
350
17
Role of fluctuations in high temperature
superconductivity
352
17.1
Phase diagram
353
17.2
Resonating valence bond theory
354
17.2.1
Strongly correlated Fermi systems
354
17.2.2
Spin-charge separation
356
17.2.3
Hidden order phase
358
17.3
Bose-metal
359
17.3.1
Staggered flux state
360
17.3.2
Vortices localization
361
17.3.3
Bipolarons
362
17.4
BCS scenarios
362
17.4.1
Strong coupling BCS-like schemes
362
17.4.2
BEOBCS scenario
363
17.5
Phenomenology
366
17.5.1
Marginal Fermi liquid
366
17.5.2
Bose
phenomenology
367
A Relations between parameters of micro- and
macroscopic theories
369
A.I Coherence length
369
A.
2
Other GL functional parameters
370
В
Properties of the
Euler
gamma function and its
logarithmic derivatives
372
B.I
Euler
gamma function
372
B.2
Digamma
function and its derivatives
372
С
Integrals of the Lawrence—Doniach theory
375
References
377
Glossary
401
Index
409
|
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| id | DE-604.BV019763069 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:05:34Z |
| institution | BVB |
| isbn | 0198528159 9780198528159 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013089379 |
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| series | International series of monographs on physics |
| series2 | International series of monographs on physics Oxford science publications |
| spelling | Larkin, Anatolij T. Verfasser aut Theory of fluctuations in superconductors Anatoly Larkin and Andrei Varlamov Oxford Clarendon Press 2005 XVIII, 412 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on physics 127 Oxford science publications Fluctuations (Physique) Supergeleidend materiaal gtt Supraconducteurs Variaties gtt Fluctuations (Physics) Superconductors Fluktuation Physik (DE-588)4130671-5 gnd rswk-swf Supraleiter (DE-588)4184140-2 gnd rswk-swf Supraleiter (DE-588)4184140-2 s Fluktuation Physik (DE-588)4130671-5 s DE-604 Varlamov, Andrei Verfasser aut International series of monographs on physics 127 (DE-604)BV000106406 127 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013089379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Larkin, Anatolij T. Varlamov, Andrei Theory of fluctuations in superconductors International series of monographs on physics Fluctuations (Physique) Supergeleidend materiaal gtt Supraconducteurs Variaties gtt Fluctuations (Physics) Superconductors Fluktuation Physik (DE-588)4130671-5 gnd Supraleiter (DE-588)4184140-2 gnd |
| subject_GND | (DE-588)4130671-5 (DE-588)4184140-2 |
| title | Theory of fluctuations in superconductors |
| title_auth | Theory of fluctuations in superconductors |
| title_exact_search | Theory of fluctuations in superconductors |
| title_full | Theory of fluctuations in superconductors Anatoly Larkin and Andrei Varlamov |
| title_fullStr | Theory of fluctuations in superconductors Anatoly Larkin and Andrei Varlamov |
| title_full_unstemmed | Theory of fluctuations in superconductors Anatoly Larkin and Andrei Varlamov |
| title_short | Theory of fluctuations in superconductors |
| title_sort | theory of fluctuations in superconductors |
| topic | Fluctuations (Physique) Supergeleidend materiaal gtt Supraconducteurs Variaties gtt Fluctuations (Physics) Superconductors Fluktuation Physik (DE-588)4130671-5 gnd Supraleiter (DE-588)4184140-2 gnd |
| topic_facet | Fluctuations (Physique) Supergeleidend materiaal Supraconducteurs Variaties Fluctuations (Physics) Superconductors Fluktuation Physik Supraleiter |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013089379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000106406 |
| work_keys_str_mv | AT larkinanatolijt theoryoffluctuationsinsuperconductors AT varlamovandrei theoryoffluctuationsinsuperconductors |