# Physics and Mathematics of Geometric Phases

## Lecture details

The lecture will be given by Professor Wegewijs and Professor Mokrousov

Description

The physics and required mathematical background of topological phases in non-relativistic quantum physics are discussed in depth. The course seeks to maintain a balance between presenting mathematical background uncommon to most physicists with profound physical applications. The course aims to be self-contained and requires basic knowledge of mathematics and band theory of solids.

Mathematical foundations

- Topological and differential manifolds

- Tensor fields

- Fiber-bundles and connections

- Homotopy, holonomy and cohomology theory

- Characteristic classes and Chern-Simons forms

Various physical applications:

- Berry phases in solids: Sundaram-Niu equations, orbital magnetization

- Berry phases in solids: Chern numbers and invariants of band manifolds

- Berry phases in solids: Quantum, spin, quantum spin, anomalous and quantum anomalous Hall effects

- Basic theory of topological insulators: topological index, bulk-surface correspondence

- Topological insulators: Key experiments

- Topological insulators: Spin-momentum locking, chiral edge states

- How to determine whether an insulator is topological or not?

- Topological insulators with broken time-reversal symmetry: How does it work?

The various interesting materials discussed in the applications include: graphene, two-dimensional and three-dimensional topological insulators.

For the time schedule, you can also refer to the university calendar:

Time | Room | Start |
---|---|---|

Mon. 1.15pm - 4.15pm |
4284 (26D 001 Hörsaal Physik) |
19.10.2015 (14 dates) |

Tues. 12.30pm - 2pm | 4273 (MBP2 015) | 20.10.2015 (14 dates) |