# Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems

## TL;DR

This paper reveals a hidden Chern number in 1D non-Hermitian chiral-symmetric systems, linking topology to in-gap end states, and demonstrates the robustness of bulk-boundary correspondence despite non-Hermitian effects.

## Contribution

It introduces a hidden Chern number in 1D non-Hermitian systems with chiral symmetry and shows its role in topologically protected end states.

## Key findings

- Hidden Chern number determines topological phases.
- End states are robust against non-Hermitian skin effect.
- Derived phase diagram for a minimal model.

## Abstract

We consider a class of one-dimensional non-Hermitian models with a special type of a chiral symmetry which is related to pseudo-Hermiticity. We show that the topology of a Hamiltonian belonging to this symmetry class is determined by a hidden Chern number described by an effective 2D Hermitian Hamiltonian $H^{\rm eff} (k, \eta)$, where $\eta$ is the imaginary part of the energy. This Chern number manifests itself as topologically protected in-gap end states at zero real part of the energy. We show that the bulk-boundary correspondence coming from the hidden Chern number is robust and immune to non-Hermitian skin effect. We introduce a minimal model Hamiltonian supporting topologically nontrivial phases in this symmetry class, derive its topological phase diagram and calculate the end states originating from the hidden Chern number.