Anomalous edge state in a non-Hermitian lattice

TL;DR

This paper explores how non-Hermiticity alters the bulk-boundary correspondence in topological insulators, revealing fractional winding numbers and unique edge states in a one-dimensional lattice with gain, loss, and long-range hopping.

Contribution

It introduces a non-Hermitian model with a fractional winding number and demonstrates the existence of a single stable edge state protected by chiral symmetry.

Findings

Fractional winding number of 1/2 in the non-Hermitian system

Existence of a single stable zero-energy edge state

Potential experimental realization with optical waveguides

Abstract

We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is described by a non-Hermitian Hamiltonian that encircles an exceptional point in momentum space. The winding number has a fractional value of 1/2. There is only one dynamically stable zero-energy edge state due to the defectiveness of the Hamiltonian. This edge state is robust to disorder due to protection by a chiral symmetry. We also discuss experimental realization with arrays of coupled resonator optical waveguides.