We provide a new and exact formalism to describe the formation of end, edge or surface states through the evolution of impurity-induced states. We propose a general algorithm that consists of finding the impurity states via the T-matrix formalism and showing that they evolve into boundary modes when the impurity potential goes to infinity. We apply this technique to obtain Majorana states, topological insulator edges states and graphene edges states. We also show that this approach provides us with a new direct and non-numerical technique to obtain the surface Green’s functions for three dimensional systems and we apply it to Weyl semimetals.

IPhT