4013414 – Advanced Seminar: Topology in Quantum Condensed Matter Physics

Advanced Seminar ("Hauptseminar") on Topology in Quantum Condensed Matter Physics will give you an opportunity to present an overview talk on the topic of your choice (see the list of topics). You already know from the courses on elementary quantum mechanics that different states can be distinguished from each other by their quantum numbers, e.g., momentum, angular momentum, etc. The appearance of these quantum numbers is closely related to symmetry-related invariance under infinitesimal transformations, e.g. under translations or rotations. The introduction of concepts of topology into physics makes it possible to identify further, so-called “topological”, quantum numbers. Topological aspects have been known in physics for a long time, from the Dirac hypothesis of the existence of magnetic monopoles (which would explain the quantization of electric charge), as well as from nuclear physics in the 1950s (“skyrmions”). However, the huge variety of topological effects and their fundamental importance as a very general and absolutely basic organizing principle in solid-state physics has become manifest recently. Today, the enormous precision of the integer quantum Hall effect (QHE) is understood as a consequence of its topological nature, as are the extraordinary properties of graphene and other novel topological materials (topological insulators, superconductors, Weyl semimetals, etc.) The fractional charge and the exotic statistics of low-lying excitations in fractional QHE are topologically determined and stabilized, as are the correlated phases of quantum spin liquids. Realizations of Majorana excitations in topological systems are of great interest, especially in the context of their potential application to topological quantum computing. Without topological concepts, modern solid state physics would be deprived of many of its most fascinating and intrinsic aspects.