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# Introduction to topological insulators

Introduction to topological insulators

Student seminar

Dr. Andor Kormanyos

Dr. Alexander Pearce

Prof. G. Burkard

Prerequisites (Voraussetzung): quantum mechanics (IK4)

Recommended (empfohlen): solid state physics (Festkörperphysik)

The theoretical framework that describes the properties of semiconductors and insulators dates back to the times of

the foundation of quantum mechanics. It has proved to be very successful - a good deal of modern semiconductor industry relies on

these early developments. However, about eight years ago it was realised that important aspects of the physics of certain

semiconductors could not be explained by the existing theory and an enhanced band theory, called "topological band theory" is needed.

The materials covered by this new theory are called "topological insulators" and they are in the focus of a very intensive current research effort.

Concepts of topological band theory have since appeared in other fields of physics as well, e.g., in particle physics and string theory.

In this seminar we are planning to cover the basic ingredients of this enhanced band theory. The emphasis will be on the understanding

of core concepts with as simple mathematical tools as possible. We will also discuss the solid state physics background that is needed to

place these concepts into a wider context.

Literature:

Lecture_Notes_arXiv:1509.02295

Rev. Mod. Phys. **82**, 1959

Brief review of 2D topological models

Seminar Topics:

The Su-Schrieffer-Heeger Model

Berry Phase and Chern Number

Adiabatic Pumping and Anomalous velocity

Two-Dimensional Chern Insulators – the Qi-Wu-Zhang Model

Time-Reversal Symmetric Two-Dimensional Topological Insulators – The Bernevig–Hughes–Zhang Model

Examples of Time-Reversal Symmetric Two-Dimensional Topological Insulators and Continuum Model of Localized States at a Domain Wall

Termine

- Vorlesung: Donnertags, P 601, 15.15
- Beginn der Vorlesung: 29.10.15
- Ende der Lehrveranstaltungen: