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Topological Aspects of Condensed Matter Physics
Last Updated: 2026-06-03 00:14:41
Abstract
The course covers various topics in the field of topological matter, such as the quantum Hall effect (integer and fractional) and symmetry protected topological insulators, but also concrete models for illustration. Methods vary from more heuristic to more mathematical ones. Concepts to be introduced include fiber bundles, Chern numbers and other indices, bulk-edge correspondence, and anyons.
Content
The course begins with the integer quantum Hall effect from various perspectives (phenomenology, heuristic explanation, role of disorder, Landau Hamiltonian, Kubo formula, Chern numbers, index of a pair of projections, bulk vs. edge). Several arguments for conductance quantization will be provided and compared, and the role of disorder addressed. Time-reversal invariant topological insulators and their indices (Fu-Kane index), as well as topological superconductors and their Majorana edge states will follow. The bigger picture provided by Kitaev's table is to be presented. Various illustrative models, though not all, are variants of graphene (Haldane, Kane-Mele, twisted bilayer graphene). The course ends with interacting systems, notably with the fractional quantum Hall effect. It is to be discussed using the Laughlin wave function, anyons, and effective field theories.
General Information
- Language
- English
- Levels
- MSC
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Topological Aspects of Condensed Matter Physics |
|
3 h weekly |