Realizing quantum anomalous Hall insulator of composite fermions in twisted bilayer graphene

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 moiré pattern in TBG could provide a tunable effective periodic potential necessary for the realization, without the need of imposing an additional superstructure as in the conventional GaAs system. It makes the TBG an ideal platform for realizing the QAHI of CFs. Based on the Dirac CF theory, we establish the phase diagram with respect to tunable experimental parameters.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 and has to be introduced as an extra parameter. Thus, the experimental realization of QAHI of CFs would be helpful for clarifying the issue, i.e., the magnetic property of CFs.