Analytical results for Green's functions of lattice fermions

Abstract: We present a further development of methods for analytical calculations of Green's functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we obtain a number of new results. In particular we derive an explicit expression for arbitrary Green's function of an open Kitaev chain and discover non-local fermionic corner states in a 2D p-wave superconductor.