  Graphene/MoS2 heterostructures are formed by combining the nanosheets of
graphene and monolayer MoS2. The electronic features of both constituent
monolayers are rather well-preserved in the resultant heterostructure due to
the weak van der Waals interaction between the layers. However, the proximity
of MoS2 induces strong spin orbit coupling effect of strength ~1 meV in
graphene, which is nearly three orders of magnitude larger than the intrinsic
spin orbit coupling of pristine graphene. This opens a bandgap in graphene and
further causes anticrossings of the spin-nondegenerate bands near the Dirac
point. Lattice incommensurate graphene/MoS2 heterostructure exhibits
interesting moire' patterns which have been observed in experiments. The
electronic bandstructure of heterostructure is very sensitive to biaxial strain
and interlayer twist. Although the Dirac cone of graphene remains intact and no
charge-transfer between graphene and MoS2 layers occurs at ambient conditions,
a strain-induced charge-transfer can be realized in graphene/MoS2
heterostructure. Application of a gate voltage reveals the occurrence of a
topological phase transition in graphene/MoS2 heterostructure. In this chapter,
we discuss the crystal structure, interlayer effects, electronic structure,
spin states, and effects due to strain and substrate proximity on the
electronic properties of graphene/MoS2 heterostructure. We further present an
overview of the distinct topological quantum phases of graphene/MoS2
heterostructure and review the recent advancements in this field.
