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(BiₓSb_1-x)₂Te₄ 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(BiₓSb_1-x)₂Te₄ 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(BiₓSb_1-x)₂Te₄ thin films is presented to help guide their experimental exploration.