Spin-orbit coupling and interactions in quantum Hall states of graphene/WSe2 heterobilayers

We use magnetotransport measurements to probe quantum Hall ground states in graphene/WSe2 heterobi-layers. Compared to pristine graphene, inter-Landau level (LL) gaps at half-filled quartets away from filling factor nu = 0 show significantly weaker dependence on the magnetic field B, while odd nu fillings show a stronger dependence. We interpret this behavior using a model incorporating Ising and Rashba spin-orbit coupling (SOC) along with Coulomb interactions within the self-consistent Hartree-Fock framework. A model fit yields Ising SOC in range similar to 1-2 meV, Rashba -10 meV, and the in-plane dielectric constant similar to 12, in agreement to previously found values. In the zeroth LL quartet, the nu = 0 gap as a function of magnetic field exhibits a plateau near 5 T, compared to similar to 20-25 T for pristine graphene. This behavior is in agreement with a model in which the SOC causes a phase transition from a canted antiferromagnetic state to a ferromagnetic state to occur at a much lower field. Our studies demonstrate how the interplay of SOC and electronic interactions affect graphene's electronic structure.