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

Abstract

We use magnetotransport measurements to probe quantum Hall ground states in graphene/${\mathrm{WSe}}_{2}$ heterobilayers. Compared to pristine graphene, inter-Landau level (LL) gaps at half-filled quartets away from filling factor $\ensuremath{\nu}=0$ show significantly weaker dependence on the magnetic field $B$, while odd $\ensuremath{\nu}$ 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 $\ensuremath{\sim}1--2 \mathrm{meV}$, Rashba $\ensuremath{\sim}10 \mathrm{meV}$, and the in-plane dielectric constant $\ensuremath{\sim}12$, in agreement to previously found values. In the zeroth LL quartet, the $\ensuremath{\nu}=0$ gap as a function of magnetic field exhibits a plateau near 5 T, compared to $\ensuremath{\sim}20--25 \mathrm{T}$ 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.