Charge order and antiferromagnetism in twisted bilayer graphene from the variational cluster approximation

Abstract

We study the possibility of charge order at quarter filling and antiferromagnetism at half-filling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek [1], relevant to a twist angle of 1.30^\circ1.30∘, and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings \frac1414, \frac1212 and \frac3434. At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion UU is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.