Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems

TL;DR

This paper extends the concept of electronic polarization to non-Hermitian systems, revealing a relationship between polarization and the winding number, and demonstrating it in a non-Hermitian SSH model.

Contribution

It introduces a biorthogonal basis-based polarization measure for non-Hermitian systems and establishes its correspondence with the winding number, including half-odd integers.

Findings

Finite polarization regions between topological phases

One-to-one correspondence between polarization and winding number

Validation in the non-Hermitian SSH model

Abstract

We discuss an extension of the Resta's electronic polarization to non-Hermitian systems with periodic boundary conditions. We introduce the ``electronic polarization'' as an expectation value of the exponential of the position operator in terms of the biorthogonal basis. We found that there appears a finite region where the polarization is zero between two topologically distinguished regions, and there is one-to-one correspondence between the polarization and the winding number which takes half-odd integers as well as integers. We demonstrate this argument in the non-Hermitian Su-Schrieffer-Heeger model.