LFU:online

Expertise on geometric phases in quantum physics and topological quantum numbers as well as basic phenomenology of topological insulators and topological superconductors

Geometric phases in quantum physics are discussed, covering Berry's phases, Aharonov Anandan phases, Pancharatnam phases, and their non-Abelian generalizations. Thereafter, the concept of topological quantum numbers is introduced with a focus on both theoretical foundations and physical phenomenology of topological insulators and topological superconductors.

Elementary methods from differential geometry and topology, single particle quantum mechanics, tight-binding models of band structures.

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

Bohm A. et al., The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics, Springer (2003).

Nakahara, M., Geometry, Topology and Physics, Taylor and Francis (2003).

Basic concepts of solid state physics, theoretical quantum physics