  Topological insulators (TIs) are a new class of matter characterized by the
unique electronic properties of an insulating bulk and metallic boundaries
arising from non-trivial bulk band topology. While the surfaces of TIs have
been well studied, the interface between TIs and semiconductors may not only be
more technologically relevant but the interaction with non-topological states
may fundamentally alter the physics. Here, we present a general model to show
that such an interaction can lead to spin-momentum locked non-topological
states, the Dirac cone can split in two, and the particle-hole symmetry can be
fundamentally broken, along with their possible ramifications. Unlike magnetic
doping or alloying, these phenomena occur without topological transitions or
the breaking of time reversal symmetry. The model results are corroborated by
first-principles calculations of the technologically relevant Bi$_2$Se$_3$ film
van der Waals bound to a Se-treated GaAs substrate.
