Non-Hermitian skin effect in periodic, random, and quasiperiodic systems

TL;DR

This paper compares how periodic, random, and quasiperiodic structures affect the non-Hermitian skin effect in quantum systems, revealing that quasiperiodicity can suppress boundary accumulation while preserving topological properties.

Contribution

It systematically analyzes the influence of different spatial structures on the NHSE using a non-Hermitian quantum walk model, highlighting the unique role of quasiperiodicity.

Findings

Periodic systems show strong boundary accumulation of bulk states.

Random systems suppress accumulation via Anderson localization but introduce in-gap states.

Quasiperiodic systems reduce boundary accumulation while maintaining a topological gap.

Abstract

The non-Hermitian skin effect (NHSE), which drives bulk states toward system boundaries, modifies bulk-boundary correspondence and complicates the identification of topological edge modes. Although breaking translational symmetry is known to influence this behavior, a systematic comparison of different structural classes remains limited. Here we investigate periodic, random, and quasiperiodic (Fibonacci) systems using a one-dimensional non-Hermitian quantum walk model. By matching the local scattering parameters in a topologically nontrivial regime, we isolate the role of spatial structure in the presence of the NHSE. We find that periodic systems exhibit pronounced boundary accumulation of bulk states. Random systems suppress this accumulation through Anderson localization, but the topological gap becomes partially filled with localized in-gap states. In contrast, the Fibonacci quasiperiodic system suppresses large-scale boundary accumulation while maintaining a well-defined topological gap. Analysis of the wave functions suggests that the hierarchical quasiperiodic structure fragments bulk states across multiple length scales, thereby mitigating the NHSE. These results identify deterministic quasiperiodicity as a distinct structural regime for controlling non-Hermitian skin dynamics and isolating topological boundary modes.