Functional renormalization group analysis of many-body states in a large moiré unit cell systems

Layers of two-dimensional materials arranged at a twist angle with respect each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states. For the exploration of these, renormalization group methods are an appropriate, flexible tool that takes into account the mutual influence of competing tendencies. We we show how the functional renormalization group known from simpler two-dimensional systems can be employed for the large-unit cell moiré superlattices, providing a description on the atomic scale and absorbing available ab-initio information on the model parameters. For the case of twisted bilayer graphene models, we explore the leading ordering tendencies depending on the band filling and the range of interactions. The results indicate a delicate balance between distinct magnetically ordered ground states.