Phenomenological Theory of twisted bilayer graphene

Twisted bilayer graphene systems have emerged as a new platform for intriguing many-body states of matter. The application of an external electric field drives the system from an insulating state to a topological state that does not conduct in bulk but does conduct on the sample edges and even to superconducting states. I will introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic-angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. Our model elucidates how the intricate form of the interactions and the particle-hole asymmetry of the electronic spectrum determine the phase diagram. It also explains how subtle differences between devices may lead to experimentally observing different behaviors. A similar model with minor modifications is suitable for describing other systems, such as untwisted and twisted trilayer Graphene and transition metal dichalcogenides structures.