  We show that electrons in ordinary III-V semiconductor double wells with an
in-plane modulating periodic potential and inter well spin-orbit interaction
are tunable Topological Insulators (TIs). Here the essential TI ingredients,
namely, band inversion and the opening of an overall bulk gap in the spectrum
arise, respectively, from (i) the combined effect of the double well even-odd
state splitting $\Delta_{SAS}$ together with the superlattice potential and
(ii) the interband Rashba spin-orbit coupling $\eta$. We corroborate our exact
diagonalization results by an analytical nearly-free electron description that
allows us to derive an effective Bernevig-Hughes-Zhang (BHZ) model.
Interestingly, the gate-tunable $\Delta_{SAS}$ drives a topological phase
transition featuring a discontinuous Chern number at $\Delta_{SAS}\sim 5.4$
meV. Finally, we explicitly verify the bulk-edge correspondence by considering
a strip configuration and determining not only the bulk bands in the
non-topological and topological phases but also the edge states and their
Dirac-like spectrum in the topological phase. The edge electronic densities
exhibit peculiar spatial oscillations as they decay away into the bulk. For
concreteness, we present our results for InAs-based wells with realistic
parameters.
