Dynamical topological invariant for non-Hermitian Rice-Mele model

TL;DR

This paper investigates a non-Hermitian Rice-Mele model, demonstrating that despite complex Berry connections, the Chern number remains quantized and can be linked to a dynamical topological invariant through adiabatic pumping.

Contribution

It introduces a dynamical topological invariant in a non-Hermitian system, extending geometric topological concepts to non-Hermitian regimes with analytical and numerical validation.

Findings

Chern number remains quantized in the non-Hermitian model.

Mid-gap edge modes obey bulk-edge correspondence.

Pumping charge acts as a dynamical topological invariant.

Abstract

We study a non-Hermitian Rice-Mele model without breaking time-reversal symmetry, with the non-Hermiticity arising from imbalanced hopping rates. The Berry connection, Berry curvature and Chern number are introduced in the context of biorthonormal inner product. It is shown that for a bulk system, although the Berry connection can be complex numbers, the Chern number is still quantized, as topological invariant. For an opened chain system, the mid-gap edge modes are obtained exactly, obeying the bulk-edge correspondence. Furthermore, we also introduce a local current in the context of biorthonormal inner product to measure the pumping charge generated by a cyclic adiabatic evolution. Analytical analysis and numerical simulation of the time evolution of the mid-gap states show that the pumping charge can be a dynamical topological invariant in correspondence with the Chern number. It indicates that the geometric concepts for Hermitian topological insulator can be extended to the non-Hermitian regime.