Superconductivity, Superfluids, and Condensates

by Annett, James F.

• ISBN13: 9780198507550
• ISBN10: 0198507550
• Format: Hardcover
• Copyright: 2004-06-03
• Publisher: Oxford University Press

Summary

The book covers three main strands, Bose-Einstein condensates (BEC), superfluids and superconductivity. The subjects are developed in a way which gradually builds up the key concepts and the necessary mathematical machinery. The book begins with the simplest of the three topics, BEC, and firstthoroughly reviews the basics of the Bose-Einstein ideal gas before going into the techniques of magnetic trapping and cooling of atoms and the discovery of BEC in dilute atomic gases. Superfluidity in helium-4 is more difficult to understand, because it is a strongly interacting quantum liquid. Thebook introduces the main physical phenomena of superfluidity, and how it follows from the key concept of macroscopic quantum coherence and off-diagonal long ranged order. The theory of superconductivity is developed in stages, starting with the simpler London and Ginzburg Landau theories and theirmain applications, before developing the mathematical concepts of a quantum coherent state and the Bardeen Cooper Schrieffer (BCS) theory. The final chapter deals with the more advanced topics, including superfluid helium-3 and evidence for unconventional Cooper pairing in exotic superconductors. Noprior knowledge of quantum many-body theory is assumed, and the necessary mathematical concepts are introduced in a self-contained manner where needed.

Table of Contents

1 Bose-Einstein condensates	1	(20)
1.1 Introduction	1	(1)
1.2 Bose-Einstein statistics	2	(4)
1.3 Bose-Einstein condensation	6	(4)
1.4 BEC in ultra-cold atomic gases	10	(7)
Further reading	17	(1)
Exercises	18	(3)
2 Superfluid helium-4	21	(26)
2.1 Introduction	21	(1)
2.2 Classical and quantum fluids	22	(4)
2.3 The macroscopic wave function	26	(1)
2.4 Superfluid properties of He II	27	(3)
2.5 Flow quantization and vortices	30	(4)
2.6 The momentum distribution	34	(4)
2.7 Quasiparticle excitations	38	(5)
2.8 Summary	43	(1)
Further reading	43	(1)
Exercises	44	(3)
3 Superconductivity	47	(20)
3.1 Introduction	47	(1)
3.2 Conduction in metals	47	(2)
3.3 Superconducting materials	49	(2)
3.4 Zero-resistivity	51	(3)
3.5 The Meissner-Ochsenfeld effect	54	(1)
3.6 Perfect diamagnetism	55	(2)
3.7 Type I and type II superconductivity	57	(1)
3.8 The London equation	58	(4)
3.9 The London vortex	62	(2)
Further reading	64	(1)
Exercises	64	(3)
4 The Ginzburg-Landau model	67	(30)
4.1 Introduction	67	(1)
4.2 The condensation energy	67	(4)
4.3 Ginzburg-Landau theory of the bulk phase transition	71	(3)
4.4 Ginzburg-Landau theory of inhomogenous systems	74	(2)
4.5 Surfaces of superconductors	76	(1)
4.6 Ginzburg-Landau theory in a magnetic field	77	(2)
4.7 Gauge symmetry and symmetry breaking	79	(2)
4.8 Flux quantization	81	(2)
4.9 The Abrikosov flux lattice	83	(6)
4.10 Thermal fluctuations	89	(4)
4.11 Vortex matter	93	(1)
4.12 Summary	94	(1)
Further reading	94	(1)
Exercises	95	(2)
5 The macroscopic coherent state	97	(30)
5.1 Introduction	97	(1)
5.2 Coherent states	98	(4)
5.3 Coherent states and the laser	102	(1)
5.4 Bosonic quantum fields	103	(3)
5.5 Off-diagonal long ranged order	106	(2)
5.6 The weakly interacting Bose gas	108	(4)
5.7 Coherence and ODLRO in superconductors	112	(4)
5.8 The Josephson effect	116	(4)
5.9 Macroscopic quantum coherence	120	(3)
5.10 Summary	123	(1)
Further reading	124	(1)
Exercises	124	(3)
6 The BCS theory of superconductivity	127	(20)
6.1 Introduction	127	(1)
6.2 The electron-phonon interaction	128	(3)
6.3 Cooper pairs	131	(3)
6.4 The BCS wave function	134	(2)
6.5 The mean-field Hamiltonian	136	(3)
6.6 The BCS energy gap and quasiparticle states	139	(4)
6.7 Predictions of the BCS theory	143	(2)
Further reading	145	(1)
Exercises	146	(1)
7 Superfluid 3He and unconventional superconductivity	147	(20)
7.1 Introduction	147	(1)
7.2 The Fermi liquid normal state of 3He	148	(4)
7.3 The pairing interaction in liquid 3He	152	(2)
7.4 Superfluid phases of 3He	154	(4)
7.5 Unconventional superconductors	158	(8)
Further reading	166	(1)
A Solutions and hints to selected exercises	167	(14)
A.1 Chapter 1	167	(2)
A.2 Chapter 2	169	(2)
A.3 Chapter 3	171	(3)
A.4 Chapter 4	174	(2)
A.5 Chapter 5	176	(2)
A.6 Chapter 6	178	(3)
Bibliography	181	(4)
Index	185