UC Santa Barbara

Remarkable phases have been observed in the magic angle twisted bilayer graphene (MATBG) systems, including correlated insulators, superconductors and quantum anomalous Hall states. In this paper, I present an integral scheme to study the interaction in TBG system at mean-field level under magnetic field. The first part mainly focuses on the non-interacting physics including the introduction and symmetry analysis in two efficient models. The second part is aimed to derive a systematic method to treat magnetic field semi-classically. By solving the Hartree-Fock kernel, different discrete symmetry breaking modes are separated that are possible to host correlated ground states. The first order phase transition from topological trivial to quantum anomalous Hall phase in the magnetic region 1.8 T to 3 T is predicted, which partially agrees with the recent experiments.