Pure skin effect obeying power partition in directed graphs

TL;DR

This paper explores a novel pure skin effect in directed graphs within non-Hermitian systems, revealing a power partition rule for decay constants and providing a generalized solution method for the skin modes.

Contribution

It introduces the concept of pure skin modes with non-oscillatory wavefunctions and a power partition rule, expanding understanding of non-Hermitian skin effects in directed graph systems.

Findings

Pure skin modes with non-oscillatory wavefunctions identified.

Decay constants follow a fixed power partition rule.

Generalized method developed for solving the generalized Brillouin zone.

Abstract

Non-Hermitian physics has received great attention recently. In particular, band structures in non-Hermitian systems can be engineered to exhibit various topological effects. Among them, one of the most intriguing phenomena is the non-Hermitian skin effect (NHSE). Here, we investigate NHSE in systems featuring directed chains or directed graphs, where the arrows denote the directions of the non-reciprocal hopping between neighbouring nodes. We show that the systems exhibit pure skin modes with non-oscillatory wavefunctions, in contrast to previously studied NHSE. Interestingly, the sum of the decay constants along different directions for each skin mode obeys a power partition rule, i.e. their sum is a fixed value and the value of each constant only depends on the ratio between the non-reciprocal hopping parameters and is independent of detailed graph configurations. Such Pure Skin Effect (PSE) can be explained by using a generalized method for solving the Generalized Brillouin-zone with multiple bulk states.