Second-Order Topological Phases in Non-Hermitian Systems

TL;DR

This paper explores second-order topological phases in non-Hermitian systems, revealing unique corner-localized modes and breakdown of usual bulk-boundary correspondence, with potential experimental realizations using ultracold atoms.

Contribution

It introduces the concept of second-order topological insulators in non-Hermitian systems and characterizes their phases using complex wavevector topological invariants.

Findings

2D non-Hermitian SOTI hosts corner zero-energy modes localized at one corner.

3D non-Hermitian SOTI supports corner modes, not along hinges.

Bulk-corner and bulk-hinge correspondence break down in non-Hermitian SOTIs.

Abstract

A $d$-dimensional second-order topological insulator (SOTI) can host topologically protected $(d - 2)$-dimensional gapless boundary modes. Here we show that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to the Hermitian case, these zero-energy modes can be localized only at one corner. A 3D non-Hermitian SOTI is shown to support second-order boundary modes, which are localized not along hinges but anomalously at a corner. The usual bulk-corner (hinge) correspondence in the second-order 2D (3D) non-Hermitian system breaks down. The winding number (Chern number) based on complex wavevectors is used to characterize the second-order topological phases in 2D (3D). A possible experimental situation with ultracold atoms is also discussed. Our work lays the cornerstone for exploring higher-order topological phenomena in non-Hermitian systems.