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You are here: Home Teaching Lectures and Seminars Summer Term 2011 Seminar on Topological States in Condensed Matter Systems

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

 

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 Spin-orbit 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

 

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