# Boundary Green functions of topological insulators and superconductors

## TL;DR

This paper introduces a recursive boundary Green function method to analyze topological insulators and superconductors, revealing their phase diagrams, edge mode localization, and topological indices across various models.

## Contribution

It develops a novel recursive approach to boundary Green functions that captures topological phases and boundary physics in a unified framework.

## Key findings

- Provides a recursive method for boundary Green functions
- Identifies fixed points corresponding to topological phases
- Applies method to models like SSH, Kitaev chain, and Chern insulator

## Abstract

Topological insulators and superconductors are characterized by their gapless boundary modes. In this paper, we develop a recursive approach to the boundary Green function which encodes this nontrivial boundary physics. Our approach describes the various topologically trivial and nontrivial phases as fixed points of a recursion and provides direct access to the phase diagram, the localization properties of the edge modes, as well as topological indices. We illustrate our approach in the context of various familiar models such as the Su-Schrieffer-Heeger model, the Kitaev chain, and a model for a Chern insulator. We also show that the method provides an intuitive approach to understand recently introduced topological phases which exhibit gapless corner states.