Special CPM Seminar

Topological insulators and superconductors present anomalous states at their boundaries

Wladimir A. Benalcazar Moncayo

Princeton University

In this talk, I will present the bulk-boundary correspondence in these phases from the perspective of Wannier centers. This framework puts first- and higher-order topological phases on equal footing and establishes the existence of a fractional density of states as the elementary boundary property, from which topological states are an inevitable consequence. I will discuss the protection of topological states in electronic, photonic, and acoustic lattices, at the boundary and at topological defects, and as mid-gap states or as “bound states in the continuum”. Finally, I will use insights from this framework to provide a notion of polarization within Chern insulators, a long-standing question in topological band theory.