# Non-Hermitian Boundary Modes

## TL;DR

This paper develops a universal Green's function-based framework to understand boundary modes in non-Hermitian systems, explaining phenomena like the skin effect and extending bulk-boundary correspondence to non-Hermitian topological phases.

## Contribution

It introduces a general, unified approach using doubled Green's functions to analyze boundary modes and topological regimes in non-Hermitian systems, surpassing previous methods.

## Key findings

- Unified Green's function formulation for boundary modes
- Explanation of skin effect in topological and non-topological systems
- Discovery of novel non-Hermitian topological regimes

## Abstract

We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green functions, we outline a generic perspective on the appearance of such modes and generate corresponding dispersion relations. In the process, we explain the skin effect in both topological and non-topological systems, exhaustively generalizing bulk-boundary correspondence in the presence of non-Hermiticity. This is accomplished via a doubled Green's function, inspired by doubled Hamiltonian methods used to classify Floquet and, more recently, non-Hermitian topological phases. Our work constitutes a general tool, as well as, a unifying perspective for this rapidly evolving field. Indeed, as a concrete application we find that our method can expose novel non-Hermitian topological regimes beyond the reach of previous methods.