Alexander Watson : Topological insulators beyond periodic structures

Posted by Christof Sparber , part of the Analysis and Applied Mathematics Seminar.

At

Oct. 7, 2019, 4 p.m.

In

636 SEO

Abstract

In the simplest case, topological insulators are two-dimensional materials which support robust, one-way, edge currents. Despite recent progress on rigorously understanding edge currents through the ``bulk-boundary correspondence’’ principle, basic practical questions about 2d materials, which are important for understanding topological insulators, remain to be answered. In this talk I will present (1) a new numerical method for computing edge states of 2d materials in the presence of edge defects, and (2) a new numerical method for computing Wannier functions of 2d materials which suggests a generalization of the ``localization-topology’’ dichotomy to general disordered (without periodic structure) 2d materials.