Seminar on Topological States in Condensed Matter Systems
Prof. Hans Kroha and Tobias Stollenwerk
Description
In many areas of physics a state is described by spatial distributions of a physical quantity, i.e., by fields. Topological states are states which are stabilized by the topology of the internal space, spanned by the values the field can take on. As a consequence, such states cannot be changed without destroying the whole system.
After several introductory talks providing the basic concepts for the description and classification of topological states, this seminar will focus on a new class of systems, which ahve been discovered only recently, whose physics is dominated by topological states: topological insulators, These are insulating materials whose surface must metallic, and the surface metal is topologically stabilized, i.e. cannot be stroyed even by impurities. Some of the exotic consequences and related experiments will be discussed.
Time and place
Tuesday, 12 c.t., SR I, HISKP
Topics
Possible topics of the individual presentations are:

Basic concepts I: homotopy groups, winding numbers

Basic concepts II: examples in solid state physics
dislocations, vortices, topological defects in higher dimensions

The Berry phase in solid state physics

Integer Quantum Hall effect

Bandstructure of Graphene: Dirac equation

Experiments on 2d topological insulators (HgCdTe quantum wells)

Homotopy classification of topological insulators

Majorana fermions at endpoints/surfaces of topological insulators

Application of Majorana fermions for quantum information processing (optional)
Literature
 M. Nakahara, Geometry, Topology and Physics (You will find a free pdf of this book over Google)
 A. Hatcher, Algebraic Topology
 D. Xiao, Berry Phase Effects on Electronic Properties
 Hasan, M. Z.; Kane, C. L. (2010). "Topological Insulators". Review of Modern Physics 82 (4): 3045
Talks
Date  Title  Speaker 
3.5  Basic concepts: homotopy groups, winding numbers and examples in solid state physics  Yuriy Stepanov 
10.5  The Berry phase in solid state physics  Daniel Klemmer 
17.5  Integer Quantum Hall effect  Yunlong Lian 
21.6  Spinorbit scattering and homotopy classification of topological insulators  Kasper Duivenvoorden 
28.6  Experiments on topological insulators  Stefan Bittihn 
5.7  Majorana fermions at endpoints/surfaces of topological insulators  Thorsten Held 
12.7  Application of Majorana fermions for quantum information processing  Anton Iakovlev 