Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes

TL;DR

This paper provides a comprehensive analytical framework for understanding higher-dimensional non-Hermitian skin and boundary modes, revealing their topological origins and the interplay between bulk and boundary phenomena.

Contribution

It introduces exact solutions and a unified approach combining amoeba theory, biorthogonal polarization, and generalized Brillouin zones for higher-dimensional non-Hermitian systems.

Findings

Analytical solutions for models in any dimension with open boundaries.

Unified understanding of skin and boundary modes through topological analysis.

Insights into the interplay between bulk and boundary phenomena in non-Hermitian systems.

Abstract

The anomalous bulk-boundary correspondence in non-Hermitian systems featuring an intricate interplay between skin and boundary modes has attracted enormous theoretical and experimental attention. Still, in dimensions higher than one, this interplay remains much less understood. Here we provide insights from exact analytical solutions of a large class of models in any dimension, $d$, with open boundaries in $d_c \le d$ directions and by tracking their topological origin. Specifically, we show that amoeba theory accounting for the separation gaps of the bulk modes augmented with higher-dimensional generalizations of the biorthogonal polarization and the generalized Brillouin zone approaches accounting for the surface gaps of boundary modes provide a comprehensive understanding of these systems.