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.
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