Bulk topological proximity effect in multilayer systems

We investigate the bulk topological proximity effect in multilayer hexagonal lattice systems by which one can introduce topological properties into a system composed of multiple trivial layers by tunnel coupling to a single nontrivial layer described by the Haldane model. In a multilayer system arrangement of different layers can significantly affect its properties. This mechanism is relevant for the bulk topological proximity effect leading to complex behavior like the emergence of dark states. The response of a trivial system to the proximity of a topological insulator appears to be highly nonlocal, in contrast to the proximity effect observed in context of superconductivity. Furthermore, for a wide range of parameters our system is semimetallic with multiple Dirac points emerging in the Brillouin zone.