Quantum anomalous Hall effect in twisted bilayer graphene quasicrystal**Project supported by the National Natural Science Foundation of China (Grant Nos. 11774325 and 21603210), the National Key Research and Development Program of China (Grant No. 2017YFA0204904), and Fundamental Research Funds for the Central Universities, China.

Abstract

The nontrivial topology is investigated in a dodecagonal quasicrystal made of 30° twisted bilayer graphene (TBG). Based on tight-binding model with both exchange field and Rashba spin–orbit coupling, the topological index, chiral edge states, and quantum conductance are calculated to distinguish its unique topological phase. A high Bott index (B = 4) quantum anomalous Hall effect (QAHE) is identified in TBG quasicrystal, which is robust to a finite perturbation without closing the nontrivial gap. Most remarkably, we have found that the multiple Dirac cone replicas in TBG quasicrystal are only a spectra feature without generating extra chiral edge states. Our results not only propose a possible way to realize the QAHE in quasicrystal, but also identify the continuity of nontrivial topology in TBG between crystal and quasicrystal.