# Topological theory of non-Hermitian photonic systems

## TL;DR

This paper introduces a gauge-independent Green function method to analyze topological invariants in non-Hermitian photonic systems, demonstrating robustness of topological properties and extending bulk-edge correspondence to these systems.

## Contribution

It develops a novel Green function approach for non-Hermitian systems, defining band-gaps and topological invariants in a gauge-independent manner.

## Key findings

- Chern number expressed as Green function integral over complex-frequency plane
- Topological properties of gyrotropic materials are robust to material loss
- Bulk-edge correspondence holds for certain non-Hermitian systems

## Abstract

Here, we develop a gauge-independent Green function approach to characterize the Chern invariants of generic non-Hermitian systems. It is shown that analogous to the Hermitian case, the Chern number can be expressed as an integral of the system Green function over a line parallel to the imaginary-frequency axis. The approach introduces in a natural way the "band-gaps" of non-Hermitian systems as the strips of the complex-frequency plane wherein the system Green function is analytical. We apply the developed theory to nonreciprocal electromagnetic continua, showing that the topological properties of gyrotropic materials are strongly robust to the effect of material loss. Furthermore, it is proven that the spectrum of a topological material cavity terminated with opaque-type walls must be gapless. This result suggests that the bulk-edge correspondence remains valid for a class of non-Hermitian systems.

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Source: https://tomesphere.com/paper/1901.01408