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 ν = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for ν = 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 10⁴ and (ii) a transition to a series of Wigner crystalline states exists as a function of ν. We find that, for ν = 1, r_s fails to cross the threshold ( r_s = 37) for the triangular lattice, and metallic transport ensues. However, for ν = 2 and ν = 3, the thresholds r_s = 22 and r_s = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (ν = 2) and a kagome (ν = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.