Quantum anomalous Hall effect in twisted bilayer graphene quasicrystal*

The nontrivial topology is investigated in a dodecagonal quasicrystal made of 30 degrees 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.