Non-Hermitian second-order topological insulator with point gap

TL;DR

This paper explores the higher-order topology of non-Hermitian systems, establishing a bulk-boundary correspondence and linking zero-mode singular states to protected corner states, revealing intrinsic topology from non-Hermiticity.

Contribution

It introduces a framework connecting zero-mode singular states to corner states in large non-Hermitian systems, extending topological understanding beyond symmetry constraints.

Findings

Zero-mode singular states correspond to protected corner states in large systems.

Winding numbers in real space count stable zero-mode singular states.

Topology can arise intrinsically from non-Hermiticity without symmetries.

Abstract

The zero-mode corner states in the gap of two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid in large-sized systems. To reveal the higher-order topology of non-Hermitian systems, we establish a correspondence between the stable zero-mode singular states and the topologically protected corner states of energy spectrum in the thermodynamic limit. Within this framework, the number of zero-mode singular values is directly linked to the number of mid-gap corner states. The winding numbers in real space can be defined to count the number of stable zero-mode singular states. Our results formulate a bulk-boundary correspondence for both static and Floquet non-Hermitian systems, where topology arises intrinsically from the non-Hermiticity, even without symmetries.