Anatomy of skin modes and topology in non-Hermitian systems

TL;DR

This paper provides a comprehensive theoretical framework for understanding boundary modes, including skin and topological modes, in non-Hermitian systems, revealing universal properties and new criteria for their existence.

Contribution

It introduces universal methods to characterize all boundary modes in non-Hermitian systems, including exact energies, decay lengths, and a new criterion for topological boundary modes.

Findings

Derived universal results for boundary modes in arbitrary non-Hermitian hopping systems.

Introduced a method to obtain exact energies and decay lengths of skin modes via imaginary flux.

Established a new generic criterion for the existence of topological boundary modes without system-specific tailoring.

Abstract

A non-Hermitian system can exhibit extensive sensitivity of its complex energy spectrum to the imposed boundary conditions, which is beyond any known phenomenon from Hermitian systems. In addition to topologically protected boundary modes, macroscopically many ``skin'' boundary modes may appear under open boundary conditions. We rigorously derive universal results for characterizing all avenues of boundary modes in non-Hermitian systems for arbitrary hopping range. For skin modes, we introduce how exact energies and decay lengths can be obtained by threading an imaginary flux. Furthermore, for 1D topological boundary modes, we derive a new generic criterion for their existence in non-Hermitian systems which, in contrast to previous formulations, does not require specific tailoring to the system at hand. Our approach is intimately based on the complex analytical properties of in-gap exceptional points, and gives a lower bound for the winding number related to the vorticity of the energy Riemann surface. It also reveals that the topologically nontrivial phase is partitioned into subregimes where the boundary mode's decay length depends differently on complex momenta roots.