# Seminar on Topological Effects in Condensed Matter Systems

## Seminar (physics655)

**Time: Thu**,** 16:00 - 18:00 **

**Place: Konferenzraum I, W 0.027, PI **

The first meeting of the seminar will be on** Thursday, April 11, 2019**.

During the first meeting on April 11, the topics will be introduced and discussed, and the talk assignments will be made.

### Overview

In everyday life, topology is often associated with the overall shape of a body, like the number of holes in a pretzel, in a cup with handle, or in a donut.

In a more mathematical language, the body is described by a mapping from a continuous coordinate space onto the surface of the body. The topological structure is then a property of that mapping, for instance, the number of holes in a body. This number cannot be altered by any continuous deformation and is, therefore, called a topological invariant.

Mappings appear also in many aspects of condensed matter physics, most prominently perhaps as the electron band structure, that is, the mapping from momentum space (Brillouin zone) to the eigenvalues or parameters of the Hamiltonian. Topological insulators, discovered experimentally several years ago, are an important class of materials with a topologically non-trivial band structure. The concept of topology in condensed matter has developed into a booming field of research and has led to a unifying view on phenomena as diverse as the quantum Hall effect (QHE), topological insulators, or graphene. In this seminar we will discuss the foundations of topology and the appearance of topological structures in various condensed matter systems, as well as their consequences for observable properties.

**Possible seminar topics include:**

- Basics of topology: topological invariants, homotopy classes, etc.
- Berry phase and topological invariants

- Topological insulators and Su-Schrieffer-Heeger (SSH) model

- Quantum Hall effect
- Floquet topological insulators: periodically driven systems and topology.

- Chern-Simons field theory
- Dirac and Weyl semimetals
- Topological superconductors
- Topology and interactions

**Representative Literature:**

B. A. Bernevig and T. L. Hughes: Topological Insulators and Topological Superconductors, Princeton University Press (2013).

**IMPORTANT NOTE:**

**The Period for registration** for a seminar course is **March 27 -- April 21, 2019**.

**Cancellation of participation** is possible until **April 28, 2019.**