Trivial and inverted Dirac bands, and emergence of quantum spin Hall states in graphene on transition-metal dichalcogenides

TL;DR

This paper investigates how proximity effects from transition-metal dichalcogenides induce spin-orbit coupling and topological states in graphene, revealing trivial and inverted band structures and the emergence of quantum spin Hall states.

Contribution

It provides first-principles analysis of proximity-induced effects in graphene on TMDCs, identifying conditions for topologically trivial and non-trivial phases, including the realization of quantum spin Hall states.

Findings

Graphene on sulfides and selenides has trivial band topology.

Graphene on WSe₂ exhibits inverted bands and topological edge states.

Quantum spin Hall effect is demonstrated in graphene on WSe₂.

Abstract

Proximity orbital and spin-orbital effects of graphene on monolayer transition-metal dichalcogenides (TMDCs) are investigated from first-principles. The Dirac band structure of graphene is found to lie within the semiconducting gap of TMDCs for sulfides and selenides, while it merges with the valence band for tellurides. In the former case the proximity-induced staggered potential gaps and spin-orbit couplings (all on the meV scale) of the Dirac electrons are established by fitting to a phenomenological effective Hamiltonian. While graphene on MoS$_2$, MoSe$_2$, and WS$_2$ has a topologically trivial band structure, graphene on WSe$_2$ exhibits inverted bands. Using a realistic tight-binding model we find topologically protected helical edge states for graphene zigzag nanoribbons on WSe$_2$, demonstrating the quantum spin Hall effect. This model also features "half-topological states", which are protected against time-reversal disorder on one edge only.