  In typical topological insulator (TI) systems the TI is bordered by a non-TI
insulator, and the surrounding conventional insulators, including vacuum, are
not generally treated as part of the TI system. Here, we implement the first
material system where the roles are reversed, and the TSS form around the
non-TI (instead of the TI) layers. This is realized by growing a layer of the
tunable non-TI $(Bi_{1-x}In_{x})_{2}Se_{3}$ in between two layers of the TI
$Bi_2Se_3$ using the atomically-precise molecular beam epitaxy technique. On
this tunable inverse topological platform, we systematically vary the thickness
and the composition of the $(Bi_{1-x}In_{x})_{2}Se_{3}$ layer and show that
this tunes the coupling between the TI layers from strongly-coupled metallic to
weakly-coupled, and finally to a fully-decoupled insulating regime. This system
can be used to probe the fundamental nature of coupling in TI materials and
provides a tunable insulating layer for TI devices.
