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)