A Green function approach to topological insulator junctions with magnetic and superconducting regions

In this work we present a Green function approach, originally implemented in graphene with well-defined edges, to the surface of a strong 3D topological insulator (TI) with a sequence of proximitized superconducting (S) and magnetic (F) surfaces. This approach consist in the calculation of the Green functions of the system by the analytical derivation of the McMillan's Green functions for each region and their coupling by a tight-binding Hamiltonian with the Dyson equation. These functions allow the direct calculation of the momentum-resolved spectral density of states, the identification of subgap interface states, and the derivation of the differential conductance for a wide variety of configurations of the junctions. We illustrate the application of this method for some simple systems with two and three regions, finding the characteristic chiral state of the anomalous quantum Hall effect (AQHE) at the N/F interfaces, and the chiral Majorana modes at the N/S interfaces. Finally we discuss some geometrical effects present in the three-region junctions such as weak Fabry-Perot resonances and Andreev bound states.