Topologie und neue Arten der Ordnung in der Physik der kondensierten Materie

What it is about

You will learn theoretical concepts and experimental signatures of topological phases in solid-state physics. In the end you will be able to distinguish phases by symmetry and topology, derive topological invariants from band structures, and understand important examples such as quantum Hall states, topological insulators and metals, as well as topological superconductors.

What you will be able to do

• Classify phases of matter by symmetry and topology
• derive topological invariants from band structures
• explain topological phenomena in the quantum Hall effect, topological insulators and topological metals
• understand axiomatic description of topological order and anyon theories
• solve exactly solvable models with topological order (e.g. toric code, string-net)
• understand fundamentals of topological quantum processing

What the module consists of

• VorlesungPresentation of theoretical foundations, methods and simple examples
• ÜbungenDiscussion and working on homework to deepen analytical skills; students discuss solutions under supervision

Teaching method

• Tafelvortrag / Blackboard lecturesfor the systematic presentation of the theoretical foundations
• Übungsaufgaben mit Heimarbeitfor deepening and practical familiarization with calculation methods
• Discussion of homework in exercisesto promote the ability to explain physical problems logically
• Schriftliche Vorlesungsunterlagen zum Downloadas a supplement and reference work