We investigate topological properties in the Fe(Te,Se) thin films. We find that the single layer ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ has nontrivial $Z_2$ topological invariance which originates from the parity exchange at the $\mathrm{\Gamma }$ point of the Brillouin zone. The nontrivial topology is mainly controlled by the Te(Se) height. Adjusting the anion height, which can be realized as the function of lattice constants and $x$ in ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$, can drive a topological phase transition. In a bulk material, the two-dimensional $Z_2$ topology invariance is extended to a strong three-dimensional one. In a thin film, we predict that the topological invariance oscillates with the number of layers. The results can also be applied to iron pnictides. Our research establishes ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ as a unique system to integrate high-$T_c$ superconductivity and topological properties in a single electronic structure.

• Received 8 July 2015
• Revised 15 December 2015

DOI:https://doi.org/10.1103/PhysRevB.93.115129