Physics and Mathematics of Geometric Phases
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.
- 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:
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)|