Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal

TL;DR

This paper explores how disorder affects topological phases in two-dimensional Ammann-Beenker quasicrystals and snub-square crystals, revealing the emergence of topological Anderson insulators and robustness of quantum spin Hall states.

Contribution

It demonstrates the existence of topological Anderson insulator phases in both quasicrystalline and crystalline lattices with disorder, highlighting their similar properties despite different symmetries.

Findings

Topological phases are robust against weak disorder in both systems.

Disorder induces topological Anderson insulator phases in both lattices.

Quantized conductance plateaus confirm the presence of topological Anderson insulators.

Abstract

The quest for the topological phases of matter in an aperiodic system has been greatly developed recently. Here we investigate the effects of disorder on topological phases of a two-dimensional Ammann-Beenker tiling quasicrystalline lattice. For comparison purposes, we also consider the case of a periodic snub-square crystalline lattice, which has the same primitive tiles as the Ammann-Beenker tiling quasicrystalline lattice. By calculating the spin Bott index and the two-terminal conductance, we confirm that the topological phases with disorder share the similar properties in the two systems which possess different symmetry and periodicity. It is shown that the quantum spin Hall states are robust against weak disorder in both the quasicrystalline lattice and the crystalline lattice. More interesting is that topological Anderson insulator phases induced by disorder appear in the two systems. Furthermore, the quantized conductance plateau contributed by the topological Anderson insulator phase is verified by the distribution of local currents.