DMS Analysis and Stochastic Analysis Seminar (SASA)

Speaker: Xiaowen Zhu (University of Washington)

Title: Bulk-edge correspondence of topological insulators with curved interfaces

Abstract: Topological insulators are central objects in condensed matter physics. They refer to insulators (i.e., Hamiltonians with a spectral gap) to which one can associate a non-trivial topological invariant. When two insulators with distinct topological invariants are glued together, the material becomes a conductor and currents flow only along the edge. Furthermore, the edge conductance is also quantized, and equals the difference of the bulk topological invariants when the edge is straight. This is the well-known bulk-edge correspondence (BEC). In this talk, we discuss BEC for topological insulators with curved interfaces. In particular, we show, for the first time, that the curved edge conductance contains geometric and electric information that can be fully separated: it is a product of two integers, each representing distinct aspects of the system.

The talk is based on joint works with Alexis Drouot.