Quantum spin Hall insulators in centrosymmetric thin films composed from topologically trivial BiTeI trilayers

The quantum spin Hall insulators predicted ten years ago and now experimentally observed are instrumental for a breakthrough in nanoelectronics due to non-dissipative spin-polarized electron transport through their edges. For this transport to persist at normal conditions, the insulators should possess a sufficiently large band gap in a stable topological phase. Here, we theoretically show that quantum spin Hall insulators can be realized in ultra-thin films constructed from a trivial band insulator with strong spin-orbit coupling. The thinnest film with an inverted gap large enough for practical applications is a centrosymmetric sextuple layer built out of two inversely stacked non-centrosymmetric BiTeI trilayers. This nontrivial sextuple layer turns out to be the structure element of an artificially designed strong three-dimensional topological insulator Bi$_2$Te$_2$I$_2$. We reveal general principles of how a topological insulator can be composed from the structure elements of the BiTeX family (X=I, Br, Cl), which opens new perspectives towards engineering of topological phases.