Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation

We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when nu = 2 or 3 charges occupy a unit moire cell, a feature attributed to Mottness per previous work but not for nu = 1, clearly inconsistent with Mott insulation. We compute r(s) = E-U/E-K, where E-U and E-K are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 10(4) and (ii) a transition to a series of Wigner crystalline states exists as a function of nu. We find that, for nu = 1, r(s) fails to cross the threshold (r(s) = 37) for the triangular lattice, and metallic transport ensues. However, for nu = 2 and nu = 3, the thresholds r(s) = 22 and r(s) = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (nu = 2) and a kagome (nu = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivitivity.