  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.
