Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way, and explores their consequences in condensed matter systems. Eschewing advanced formal methods, the author uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-paired systems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity; the physical systems discussed include liquid 4-He, the BEC alkali gases, "classical" superconductors, superfluid 3-He, "exotic" superconductors and the recently stabilized Fermi alkali gases.The book should be accessible to beginning graduate students in physics or advanced undergraduates.
Author(s): Anthony James Leggett
Series: Oxford Graduate Texts
Publisher: Oxford University Press, USA
Year: 2006
Language: English
Pages: 408
Contents......Page 10
Preface......Page 6
List of symbols......Page 12
1 Quantum liquids......Page 18
1.1 Indistinguishability and the symmetry of the many-body wave function......Page 20
1.2 The Fermi–Dirac and Bose–Einstein distributions: BEC in a noninteracting gas......Page 25
1.3 Cooper pairing......Page 30
1.4 The experimental systems......Page 32
1.5 Superconductivity and superfluidity: basic phenomenology......Page 37
Appendix......Page 43
2.1 Definition of BEC in an interacting system......Page 48
2.2 The order parameter and the superfluid velocity; alternative definitions of BEC......Page 51
2.3 Why should BEC occur in an interacting system? When does it (not)?......Page 57
2.4 Pseudo-BEC in a Fermi system (Cooper pairing)......Page 63
2.5 The consequences of BEC: preview of coming attractions......Page 70
2.6 Fragmented BEC......Page 77
Appendices......Page 80
3 Liquid [sup(4)]He......Page 88
3.1 Anomalous properties of the He-II phase......Page 89
3.2 Direct evidence for BEC in He-II......Page 90
3.3 The two-fluid model of He-II: static effects......Page 93
3.4 The two-fluid model: dynamical effects......Page 100
3.5 Quantized vortices, phase slip and the Josephson effect......Page 108
3.6 The excitation spectrum of liquid He-II......Page 115
3.7 Microscopic theories of He-II......Page 119
4.1 The atoms: structure, trapping, and diagnostics......Page 130
4.2 s-wave scattering and effective interaction......Page 135
4.3 The Gross–Pitaevskii equation: some simple applications......Page 140
4.4 The Bogoliubov approximation......Page 148
4.5 Coherence and interference in dilute alkali Bose gases......Page 151
4.6 Optical lattices......Page 162
4.7 Signatures of superfluidity in the BEC alkali gases......Page 167
Appendix......Page 174
5.1 The normal state......Page 182
5.2 The effective electron–electron interaction......Page 187
5.3 The Cooper instability......Page 192
5.4 BCS theory at T = 0......Page 195
5.5 Excited states and finite-temperature BCS theory......Page 203
5.6 The two-fluid model for superconductors: the Meissner effect......Page 207
5.7 The Ginzburg–Landau theory......Page 215
5.8 Generalizations of BCS: the “non-pair-breaking” case......Page 225
5.9 Pair-breaking effects......Page 233
5.10 The Josephson effect......Page 240
Appendix......Page 245
6.1 The normal phase of liquid [sup(3)]He......Page 268
6.2 Anisotropic Cooper pairing......Page 271
6.3 Generalized Ginzburg–Landau approach: spin fluctuation feedback......Page 277
6.4 Spontaneously broken spin–orbit symmetry and spin dynamics......Page 282
6.5 Supercurrents, textures and defects......Page 289
7.1 Introduction......Page 300
7.2 The cuprates: composition, structure, and phase diagram......Page 301
7.3 The cuprates: principal experimental properties......Page 312
7.4 Normal state at optimal doping......Page 313
7.5 The “pseudogap” regime......Page 319
7.6 Superconducting state......Page 321
7.7 Some preliminary comments on the experimental data......Page 330
7.8 What do we know for sure about cuprate superconductivity?......Page 331
7.9 The cuprates: questions and ideas......Page 343
7.10 Novel consequences of Cooper pairing in the cuprates......Page 353
Appendices......Page 363
8.1 Noncuprate “exotic” superconductors......Page 366
8.2 Liquid [sup(3)]He in aerogel......Page 372
8.3 Supersolids......Page 375
8.4 Fermi alkali gases: the BEC-BCS crossover......Page 381
Appendix......Page 388
Bibliography......Page 390
B......Page 398
D......Page 399
G......Page 400
J......Page 401
N......Page 402
P......Page 403
S......Page 404
Z......Page 405
