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The quantum spin Hall insulators predicted ten years ago and nowexperimentally observed are instrumental for a breakthrough in nanoelectronicsdue to non-dissipative spin-polarized electron transport through their edges.For this transport to persist at normal conditions, the insulators shouldpossess a sufficiently large band gap in a stable topological phase. Here, wetheoretically show that quantum spin Hall insulators can be realized inultra-thin films constructed from a trivial band insulator with strongspin-orbit coupling. The thinnest film with an inverted gap large enough forpractical applications is a centrosymmetric sextuple layer built out of twoinversely stacked non-centrosymmetric BiTeI trilayers. This nontrivial sextuplelayer turns out to be the structure element of an artificially designed strongthree-dimensional topological insulator Bi$_2$Te$_2$I$_2$. We reveal generalprinciples of how a topological insulator can be composed from the structureelements of the BiTeX family (X=I, Br, Cl), which opens new perspectivestowards engineering of topological phases.

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