# Analytical results for Green's functions of lattice fermions

## TL;DR

This paper develops analytical methods using recurrence relations to compute Green's functions of lattice fermions, leading to new explicit formulas and the discovery of non-local corner states in topological superconductors.

## Contribution

It introduces a recurrence relation approach for analytical Green's functions, providing explicit formulas and novel insights into topological phases.

## Key findings

- Explicit Green's function for open Kitaev chain derived
- Non-local fermionic corner states identified in 2D p-wave superconductor
- Enhanced analytical tools for lattice fermion systems

## 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.