The nature of correlations in the insulating states of twisted bilayer graphene

Abstract

The recently observed superconductivity in twisted bilayer graphene emerges\nfrom insulating states believed to arise from electronic correlations. While\nthere have been many proposals to explain the insulating behaviour, the\ncommensurability at which these states appear suggests that they are Mott\ninsulators. Here we focus on the insulating states with $\\pm 2$ electrons or\nholes with respect to the charge neutrality point. We show that the theoretical\nexpectations for the Mott insulating states are not compatible with the\nexperimentally observed dependence on temperature and magnetic field if, as\nfrequently assumed, only the correlations between electrons on the same site\nare included. We argue that the inclusion of non-local (inter-site)\ncorrelations in the treatment of the Hubbard model can bring the predictions\nfor the magnetic and temperature dependencies of the Mott transition to an\nagreement with experiments and have consequences for the critical interactions,\nthe size of the gap, and possible pseudogap physics. The importance of the\ninter-site correlations to explain the experimental observations indicates that\nthe observed insulating gap is not the one between the Hubbard bands and that\nantiferromagnetic-like correlations play a key role in the Mott transition.\n