The Periodic Table for Topological Insulators and Superconductors (3/3)

Date

Jun 20, 2014

Time

1:00 PM - 2:30 PM

Speaker

Dr. Jens Bardarson

Affiliation

Max Planck Institute for the Physics of Complex Systems, Dresden

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. R. Schilling / Dipl.-Math J. Hollender

Description

Ein Vortrag im Rahmen der "Graduate Lectures in Mathematics" Quantum mechanics is perhaps the most successful theory that physicists have ever conceived of. The quantum theory of solids, in particular, predicts and explains the difference between metals and insulators in terms of their so-called band structure. Surprisingly, it was only in the last few years that it was fully realized that not all insulators are the same. Rather, there are distinct classes of insulators that differ in the topology of their "electronic band structure". This has fundamental consequences: topological insulators are bulk insulators that have a stable and robust metallic surface. Similarly, topological superconductors realize exotic edge states that could potentially be used in future quantum computers. In these set of lectures we discuss some of the mathematical structures needed to classify all possible topological insulators and superconductors and thereby construct their "periodic table". The focus will be on the use of the concepts rather than attempting to formally and rigorously define them. No prior knowledge of quantum theory will be assumed and the few concepts needed are explained as they come along. The main mathematical constructs needed originate in group theory and, not surprisingly, topology.

Links

• Webseite der Graduate Lectures in Mathematics

Last modified: Apr 8, 2014, 6:05:48 PM