Valley order and loop currents in graphene on hexagonal boron nitride

We examine the role of Coulomb interactions in the emergence of macroscopically ordered states in graphene supported on hexagonal boron nitride substrates. Due to incommensuration effects with the substrate and interactions, graphene can develop gapped low-energy modes that spatially conform into a triangular superlattice of quantum rings. In the presence of these modes, we show that Coulomb interactions lead to spontaneous formation of chiral loop currents in bulk and to macroscopic spin-valley order at zero temperature. We show that this exotic state breaks time-reversal symmetry and can be detected with interferometry and polar Kerr measurements.