Quantum anomalous Hall insulator of composite fermions in twisted bilayer graphene

Abstract We theoretically study the realization of quantum anomalous Hall insulator (QAHI) of composite fermions (CFs) in the twisted bilayer graphene (TBG) system. We show that the moir\'e pattern in TBG is not only able to provide a commensurate moir\'e superlattice, but also a tunable effective periodic potential necessary for the realization, without the need of imposing an additional superstructure as in the conventional GaAs system. These make the TBG an ideal platform for realizing the QAHI of CFs. We establish the phase diagram with respect to tunable experimental parameters based on the Dirac CF theory. We find that the topological property of the system depends critically on the orbital magnetic susceptibility of CFs, which is not specified in the pristine Dirac CF theory. The experimental realization of QAHI of CFs would be helpful for unveiling the magnetic property of CFs and clarifying the issue.