Magnetic perturbation theory and topological insulators
Tuesday 28 January 2020
Magnetic Schrödinger operators are often used as a model to describe the phenomenology of topological insulators. In this context, an important role is played by perturbations given by a constant magnetic field. Nevertheless, due to their singular character, such magnetic perturbations cannot be treated using standard perturbation theory techniques. A solution to this problem is given by gauge covariant magnetic perturbation theory, which was developed by H. Cornean and G. Nenciu during the 2000s and it will be presented in the first part of the talk. After that, as an application of this theory to topological insulators, I will show the proof of a gap labelling theorem for Bloch-Landau Hamiltonians. The talk is based on a joint work with H. Cornean and D. Monaco.