Non-Hermitian quasicrystalline topological insulators

TL;DR

This paper investigates how non-Hermiticity affects topological insulators in quasicrystalline lattices, revealing new ways to manipulate edge and corner states, with implications for future quantum materials.

Contribution

It introduces the study of non-Hermitian effects on topological insulators within quasicrystals, focusing on asymmetric hopping and its impact on boundary state distribution.

Findings

Asymmetric hopping alters edge state distribution in quasicrystals.

Higher-order topological corner states are robust under non-Hermitian perturbations.

Distribution of boundary states can be controlled by symmetry adjustments.

Abstract

In recent years, the interplay between non-Hermiticity and band topology is expected to uncover numerous novel physical phenomena. However, the majority of research has focused on periodic crystalline structures, with comparatively fewer studies exploring quasicrystalline systems. In this paper, we delve into the influence of asymmetric hopping on the topological insulators, specifically focusing on quantum spin Hall insulators and higher-order topological insulators in an octagonal Ammann-Beenker quasicrystalline lattice. We demonstrate that asymmetric hopping can significantly alter the distribution of edge states, leading to a uniform distribution across all boundaries or localizing them at a single edge, depending on the symmetry adjustments. Furthermore, we explore the robustness of higher-order topological corner states under perturbations, showing that these states can maintain their distribution even in the presence of non-Hermiticity. Our findings not only expand the current understanding of topological states in quasicrystals under non-Hermitian conditions, but also provide valuable theoretical guidance for manipulating corner state distributions in non-Hermitian quasicrystalline higher-order topological insulators.