  The so called quantum spin Hall phase is a topologically non trivial
insulating phase that is predicted to appear in graphene and graphene-like
systems. In this work we address the question of whether this topological
property persists in multilayered systems. We consider two situations: purely
multilayer graphene and heterostructures where graphene is encapsulated by
trivial insulators with a strong spin-orbit coupling. We use a four orbital
tight-binding model that includes the full atomic spin-orbit coupling and we
calculate the $Z_{2}$ topological invariant of the bulk states as well as the
edge states of semi-infinite crystals with armchair termination. For
homogeneous multilayers we find that even when the spin-orbit interaction opens
a gap for all the possible stackings, only those with odd number of layers host
gapless edge states while those with even number of layers are trivial
insulators. For the heterostructures where graphene is encapsulated by trivial
insulators, it turns out that the interlayer coupling is able to induce a
topological gap whose size is controlled by the spin-orbit coupling of the
encapsulating materials, indicating that the quantum spin Hall phase can be
induced by proximity to trivial insulators.
