Topological phases and twisting of graphene on a dichalcogenide monolayer

Graphene placed in proximity to a transition metal dichalcogenide semiconductor monolayer has been shown to exhibit interesting modifications of its electronic properties. The role of incommensurability and a possible relative twist between layers require implementing a continuum model approach to fully investigate this multilayered system. Results of this model are in agreement with simplified approaches, such as the tight-binding model, that assumes commensurate supercells. We show that the misaligned system can also exhibit multiple different topological phases depending on the relative twist angle and applied gate voltages between the layers[1]. An interesting topological phase exhibits inverted bands which is robust to incommensurate structure effects.
Using an effective Hamiltonian to fully describe the continuum model of graphene-TMD heterostructure reveals that a staggered potential and effective SOC are induced onto the graphene, which controls the appearance of the non-trivial topological phase. Our estimates suggest that the intrinsic SOC induced onto graphene deposited on typical TMDs is somewhat weak and must be enhanced by additional means, such as heavy metal intercalation, to achieve a tunable quantum spin Hall phase.
[1]A. Alsharari, et.al, arXiv:1808.06662, (2018)