  The search for strongly inversion asymmetric topological insulators is an
active research field because these materials possess distinct properties
compared with the inversion symmetric ones. In particular, it is desirable to
realize a large Rashba spin-splitting (RSS) in such materials, which combined
with the topological surface states (TSS) could lead to useful spintronics
applications. In this report, based on first principles calculations, we
predict that the heterostructure of BiTeI/Bi$_{2}$Te$_{3}$ is a strong
topological insulator with a giant RSS. The coexistence of TSS and RSS in the
current system is native and stable. More importantly, we find that both the
$\mathbb{Z}_{2}$ invariants and the Rashba energy can be controlled by
engineering the layer geometries of the heterostructure, and the Rashba energy
can be made even larger than that of bulk BiTeI. Our work opens a new route for
designing topological spintronics devices based on inversion asymmetric
heterostructures.
