Hartree Fock study of insulating states in twisted bilayer graphene using hybrid Wannier basis

In this work, the insulating behavior of twisted bilayer graphene and in particular the quantum anomalous Hall state has been studied; the effects of electron-electron interaction are taken into account by performing a Hartree-Fock analysis which is the standard approach for finding symmetry broken states. The model is truncated to the active relevant bands and the study is done using the basis of maximally localized Hybrid Wannier functions; this basis on the one hand respects important symmetries of the system, and on the other hand makes the interaction local at least in one direction. It also implies that the geometry of the system is that of a cylinder. Furthermore, by tuning the form/strength of the interaction, we are able to predict some other interesting phases which might potentially be found in the future.