We provide here a direct and exact formalism to describe the formation of edge or surface states, as well as to calculate boundary Green's functions. Modeling the boundary as an impurity potential, we show via the T-matrix formalism that the impurity states evolve into boundary modes when the impurity potential goes to infinity. We apply this technique to obtain Majorana states in one- (1D) and two-dimensional Kitaev systems. For the 1D case we also calculate the corresponding boundary Green's functions. We argue that our formalism can be applied to other topological models, as well as to any model exhibiting edge states.

• Received 20 November 2018

DOI:https://doi.org/10.1103/PhysRevB.100.081106