Valley magnetism, density waves, and nematicity in twisted bilayer graphene

We analyze density wave and Pomeranchuk orders in twisted bilayer graphene. We assume that near half filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. Another state is valley-polarized charge order. In the absence of additional perturbations these terms are degenerate. Introducing degeneracy-lifting terms we consider potential ground states. For the magnetic state, a subleading intervalley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong-coupling approaches, indicating that this order is robust. For valley-polarized charge order there is a coexistence phase with magnetism which realizes valley-polarized magnetic order. In addition, we find a weaker but still attractive interaction in nematic channels and discuss the type of a nematic order.