Thouless.Les.Houches.Intro to topological quantum numbers

1.1 Precision and topological invariants......Page 3
1.2 Winding numbers and line defects......Page 4
1.3 Homotopy groups and defect classification......Page 6
2.1 Quantized vortices and flux lines......Page 9
2.2 Detection of quantized circulation and flux......Page 15
2.3 Precision of circulation and flux quantization measurements......Page 18
3.1 Magnus force and two-fluid model......Page 20
3.2 Vortex moving in a neutral superfluid......Page 22
3.3 Transverse force in superconductors......Page 26
4.1 Introduction......Page 28
4.2 Proportionality of current density and electric field......Page 29
4.3 Bloch’s theorem and the Laughlin argument......Page 30
4.4 Chern numbers......Page 33
4.5 Fractional quantum Hall effect......Page 37
4.6 Skyrmions......Page 40
5.1 The vortex induced transition in superfluid helium films......Page 41
5.2 Two-dimensional magnetic systems......Page 47
5.3 Topological order in solids......Page 48
5.4 Superconducting films and layered materials......Page 51
6.1 Vortices in the A phase......Page 53
6.2 Other defects and textures......Page 57
7.1 Order in liquid crystals......Page 60
7.2 Defects and textures......Page 62
References......Page 68