Non-Hermitian quasicrystalline topological insulators

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.