Projectively topological exceptional points in non-Hermitian Rice-Mele model

TL;DR

This paper investigates the topological nature of exceptional points in a non-Hermitian Rice-Mele model, revealing that their topological properties persist even in finite and quasi-1D systems, linking them to 2D topological invariants.

Contribution

It demonstrates that topological characteristics of exceptional points in a 2D non-Hermitian system are preserved in finite and quasi-1D systems, establishing a connection between 1D and 2D topological invariants.

Findings

Exceptional points exhibit topological charges of ±1/2.

Topological properties remain in finite and quasi-1D systems.

Topological invariants can be derived from 2D limits and projected onto 1D systems.

Abstract

We study coupled non-Hermitian Rice-Mele chains, which consist of Su-Schrieffer-Heeger (SSH) chain system with staggered on-site imaginary potentials. In two dimensional (2D) thermodynamic limit, the exceptional points (EPs) are shown to exhibit topological feature: EPs correspond to topological defects of a real auxiliary 2D vector field in k space, which is obtained from the Bloch states of the non-Hermitian Hamiltonian. As a topological invariant, the topological charges of EPs can be $\pm$1/2, obtained by the winding number calculation. Remarkably, we find that such a topological characterization remains for a finite number of coupled chains, even a single chain, in which the momentum in one direction is discrete. It shows that the EPs in the quasi-1D system still exhibit topological characteristics and can be an abridged version for a 2D system with symmetry protected EPs that are robust in perturbations, which proves that topological invariants for a quasi-1D system can be extracted from the projection of the corresponding 2D limit system on it.