Quantum spin Hall states in graphene interacting with WS$_2$ or WSe$_2$

In the framework of first-principles calculations, we investigate the structural and electronic properties of graphene in contact with as well as sandwiched between WS$_2$ and WSe$_2$ monolayers. We report the modification of the band characteristicsdue to the interaction at the interface and demonstrate that the presence of the dichalcogenides results in quantum spin Hall states in the absence of a magnetic field.