Effect of Intervalley Interaction on Band Topology of Commensurate Graphene/EuO Heterostructures
Recent experiments demonstrating proximity induced ferromagnetism in graphene motivate this study of commensurate graphene/EuO heterostructures. Due to the commensurability of graphene with the (111)-EuO layer, graphene’s Dirac points are mapped to the Γ point of the commensurate Brillouin zone. The Eu atoms not only induce proximity exchange on the graphene layer, but they also introduce intervalley interactions resulting in a nonlinear dispersion at Γ. We develop a model Hamiltonian, consistent with the lattice symmetries, that includes proximity induced exchange splitting, spin-orbit coupling, and intervalley interactions with parameters fitted to ab initio calculations. The intervalley interaction opens up a trivial gap preventing the system from
crossing into a nontrivial state. The model Hamiltonian is analyzed to determine the conditions under which the heterostructures can exhibit topologically nontrivial bands.