Wigner Crystallization in lieu of Mottness in Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) exhibits dispersionless bands at a particular set of twist values called magic angles. This dispersionless behavior can be understood from an effective description of the bilayer system in terms of a triangular superlattice formed by the so called Moir\'e patterns. The kinetic energy of the quasi-free electrons in this superlattice is heavily quenched, causing the interactions to dominate, and thus rendering TBG a playground of strong correlation physics. Although it has been argued [1-5] that the novel insulating state arising from such twist angles is of the Mott-type, we show here that the the insulating state in the vicinity of the magic angles is actually a Wigner crystal. The Mott state obtains at a density four orders of magnitude larger that in the experimental systems, thereby rendering it irrelevant to the physics of TBG near the magic angles. Superconductivity then arises from melting (doping) a Wigner crystal which has been argued previously [6] to exhibit superconducting correlations. Defect-mediated melting in a Wigner crystal should exhibit strong Berezinskii-Kosterlitz-Thouless behaviour and hence should serve as a guide to the experiments.