Edge modes at soft walls

Charlista: Hanne Van Den Bosch - Departamento de Ingeniería Matemática & Centro de Modelamiento Matemático, U. de Chile

Resumen: This talk concerns tight-binding models that describe periodic structures terminated by a soft wall. Our main examples are the one-dimensional SSH chain and the two-dimensional Wallace model for graphene. The soft wall is just a potential that increases smoothly to infinity on one side, thus forbidding propagation to that side. Our goal is to show how this potential creates "edge modes", that have energies in the gaps of the bulk spectrum, and to estimate their number. The main conclusion is that the appearance of edge modes is independent of the details of the model, and their presence can be detected by a spectral flow argument. I will introduce this method in a qualitative way without the need for mathematical preliminaries.