Physics and Mathematics of Geometric Phases


Lecture details

The lecture will be given by Professor Wegewijs and Professor Mokrousov


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)