Electronic polarization in non-Bloch band theory

TL;DR

This paper introduces the non-Bloch polarization as a topological measure to understand the non-Hermitian skin effect and extends the non-Bloch bulk-boundary correspondence to two-dimensional systems with spiral boundary conditions.

Contribution

It proposes the non-Bloch polarization as a new topological quantity and explores its role in non-Hermitian systems, including 2D models.

Findings

Non-Bloch polarization detects the non-Hermitian skin effect.

Extension of non-Bloch bulk-boundary correspondence to 2D systems.

Application to non-Hermitian Su-Schrieffer-Heeger model.

Abstract

Hermitian topological materials are characterized by the nontrivial relation between topological numbers and edge modes, i.e. the bulk-boundary correspondence. In non-Hermitian systems, the conventional correspondence breaks down. Instead, in the non-Hermitian Su-Schrieffer-Heeger model, the non-Bloch bulk-boundary correspondence, which is the relation between the non-Bloch winding number and the non-Hermitian skin effect, is proposed by S. Yao and Z. Wang. We introduce the non-Bloch polarization as a topological quantity to detect the non-Hermitian skin effect. Moreover, we also discuss the non-Bloch bulk-boundary correspondence in two-dimensional systems using the non-Bloch polarization with spiral boundary conditions.