# Surface Green's functions and boundary modes using impurities: Weyl semimetals and topological insulators

## TL;DR

This paper introduces a new analytical method to compute surface Green's functions for 3D topological systems, enabling precise analysis of boundary states like Fermi arcs without numerical approximations.

## Contribution

The authors develop a direct, non-numerical technique based on T-matrix formalism to obtain surface Green's functions for topological insulators and Weyl semimetals.

## Key findings

- Calculated surface Green's functions for Weyl semimetals.
- Analyzed Fermi-arc surface states.
- Extended method to Kane-Mele and Chern insulators.

## Abstract

In this work we provide a new direct and non-numerical technique to obtain the surface Green's functions for three-dimensional systems. This technique is based on the ideas presented in Phys. Rev. B 100, 081106(R), in which we start with an infinite system and model the boundary using a plane-like infinite-amplitude potential. Such a configuration can be solved exactly using the T-matrix formalism. We apply our method to calculate the surface Green's function and the corresponding Fermi-arc states for Weyl semimetals. We also apply the technique to systems of lower dimensions, such as Kane-Mele and Chern insulator models, to provide a more efficient and non-numerical method to describe the formation of edge states.