Topological phase transition and two-dimensional topological insulators in Ge-based thin films

We discuss possible topological phase transitions in Ge-based thin films of Ge(BixSb1-x)(2)Te-4 as a function of layer thickness and Bi concentration x using the first-principles density functional theory framework. The bulk material is a topological insulator at x = 1.0 with a single Dirac cone surface state at the surface Brillouin zone center, whereas it is a trivial insulator at x = 0. Through a systematic examination of the band topologies, we predict that thin films of Ge(BixSb1-x)(2)Te-4 with x = 0.6, 0.8, and 1.0 are candidates for two-dimensional (2D) topological insulators, which would undergo a 2D topological phase transition as a function of x. A topological phase diagram for Ge(BixSb1-x)(2)Te-4 thin films is presented to help guide their experimental exploration.