Stacking Effects on Graphene and Dichalcogenide Hybrid Structures

Topological properties of heterostructures of graphene (G) and transition metal dichalcogenides (TMDs) have been the center of recent interest [1]. Here we study bilayers and trilayers of G and TMD and show that stacking and ordering is crucial to the resulting band structure of the system and its consequent topology. To analyze the topological properties of these systems we adopt a tight binding formalism that allows a complete topological characterization, including Chern numbers and Z₂ index, and helps to explicitly confirm the existence of edge states in these systems. A G-TMD heterostructure displays a phase transition that allows for the appearance of gapless edge states [1]. However, a Bernal stacked bilayer graphene deposited on a TMD monolayer is found to not host gapless edge states. We show that the crucial factor determining the appearance of edge states in such systems is the relative strength of the diagonal Zeeman-like spin-orbit term inherited from the TMD and the staggered potential on graphene generated also by proximity.

[1] A.M. Alsharari et al, PRB 94, 241106(R) (2016).