Characterizing the topological properties of one-dimensional non-hermitian systems without the Berry-Zak phase

TL;DR

This paper introduces a novel complex-plane method to predict topological phases in 1D non-Hermitian systems, bypassing the Berry-Zak phase, and enabling easier analysis of topological transitions.

Contribution

It presents a new approach using poles and zeros of a complex function derived from Bloch waves to characterize topological properties without relying on the Berry-Zak phase.

Findings

The method can predict topological phase transitions.

It extends topological analysis to non-Hermitian systems.

The approach simplifies the characterization process.

Abstract

A new method is proposed to predict the topological properties of one-dimensional periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and zeros. The sequence of poles and zeros of this function is a topological invariant that can be linked to the Berry-Zak phase. Since the characterization of the topological properties is done in the complex plane, it can easily be extended to the case of non-hermitian systems. The sequence of poles and zeros allows to predict topological phase transitions.