Non-Hermitian second-order skin and topological modes

TL;DR

This paper develops an analytical nested tight-binding formalism to precisely describe second-order topological corner modes and skin effects in non-Hermitian systems, providing exact solutions and validation across models.

Contribution

It introduces a novel nested tight-binding approach for analyzing second-order topological modes in non-Hermitian systems, enabling exact solutions without additional assumptions.

Findings

Exact solutions for second-order topological zero-energy corner modes.

Validation of the formalism in hybrid skin-topological modes.

Illustration of corner modes induced by second-order skin effect.

Abstract

The skin effect and topological edge states in non-Hermitian system have been well-studied, and the second-order skin effect and corner modes have also been proposed in non-Hermitian system recently. In this paper, we construct the nested tight-binding formalism to research the second-order corner modes analytically, which is a direct description of the generic non-Hermitian tight-binding model without other assumptions. Within this formalism, we obtain the exact solutions of second-order topological zero-energy corner modes for the non-Hermitian four-band model. We validate the nested tight-binding formalism in the hybrid skin-topological corner modes for the four-band model and a non-Hermitian two-dimensional (2D) extrinsic model. In addition, we exactly illustrate the corner modes induced by second-order skin effect for a simplest 2D non-Hermitian model by the nested tight-binding formalism.