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We study the ground-state properties of twisted bilayer graphene. The low-energy single-electron spectrum consists of weakly dispersing partially degenerate bands, making electrons susceptible to the effects of interactions. Introducing several order parameters with spin-density-wave-like structure, we demonstrate that (i) the band degeneracy is partially lifted, and (ii) the low-energy spectrum becomes doping-dependent. Such sensitivity to doping allows us to reproduce qualitatively the behavior of the conductance observed in experiments. Near half-filling, the hexagonal symmetry is lost, and a nematic state appears, that is robust against variations of the interlayer hopping amplitude.
Sergio Caprara