## Competition of trivial and topological phases in graphene based hybrid systems

Tuning spin-orbit interaction in graphene samples promises several revolutionary applications. One of the most striking effects is the appearance of a quantum spin Hall phase as proposed by Kane and Mele. Since the intrinsic spin-orbit coupling is weak in graphene one needs to turn to alternative methods in order to reach the topological phase. Combining graphene with other novel layered materials is a possible way for engineering the band structure of charge carriers. Strong spin-orbit coupling in BiTeX compounds and the recent fabrication of a single layer of BiTeI points towards a feasible experimental realization of a Kane-Mele phase in graphene-based heterostructures. In our previous work, we explored the electronic structure and topological phase diagram of hybrid systems built from graphene and BiTeX (X=I, Br, Cl) layers. We showed that structural stress inherently present in fabricated samples could easily induce a topological phase transition thus turning the sample in a novel experimental realization of a time reversal invariant topological insulator. During the talk I would like to show a model that captures the essence of the undergoing physical processes in these systems focusing on the low-energy degrees of freedom of the perturbed graphene lattice.