Condensed matter · PDF notes
Topology in condensed-matter physics
A consolidated guide to topological phases, topological defects, and Landau theory of phase transitions.
This collection brings together three compact references: topology in condensed-matter systems, topological defects in ordered media, and the Landau description of phase transitions. Together they connect global geometric structure, the classification of singular configurations, and symmetry-breaking order parameters.
Topology in condensed-matter physics
- Berry curvature and its symmetry properties
- Why insulating gaps matter for topological invariants
- Chern numbers and transverse Hall response
- The SSH model, winding numbers, and edge modes
- Level crossings and topological phase transitions
- Integer quantum Hall physics
- Jackiw-Rebbi solutions and anti-unitary symmetries
Topological defects
- Order-parameter spaces and continuous deformations
- The role of homotopy groups in classifying defects
- Point, line, and texture-like defects
- Examples from nematics, superfluids, and XY models
Landau theory of phase transitions
- Continuous and first-order transitions in a mean-field description
- Order parameters and spontaneous symmetry breaking
- Free-energy expansions and stability of ordered phases
- Why Landau theory becomes unreliable close to a critical point
Use the topology PDF as a map of topological band theory, the defects PDF to translate symmetry-breaking problems into homotopy classifications, and the Landau PDF to compare these ideas with conventional phase transitions.