Mathematical and Physical Aspects of Topologically Protected States

Bulk-edge correspondence in the presence of a mobility gap

Gian Michele Graf

ETH Zurich
[SLIDES]

Band insulators are characterized by the Fermi energy lying in spectral gap. More generally, we consider situations where that energy lies within the spectrum, though in an regime of localization. We discuss how indices are defined and affected by that situation, as well as the relation between edge and bulk. The discussion is pedestrian and is based on examples in dimension 1 and 2 exhibiting different symmetries.