Heterostructures of Dirac materials such as graphene and topological insulators provide interesting platforms to explore exotic quantum states of electrons in solids. Here we study the electronic structure of graphene-Sb2Te3 heterostructure using density functional theory and tight-binding methods. We show that the epitaxial graphene on Sb2Te3 turns into quantum spin-Hall phase due to its proximity to the topological insulating Sb2Te3. It is found that the epitaxial graphene develops a giant spin-orbit gap of about ~20 meV, which is about three orders of magnitude larger than that of pristine graphene. We discuss the origin of such enhancement of the spin-orbit interaction and possible outcomes of the spin-Hall phase in graphene.

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