Splitting of the topologically-protected Dirac cone without breaking time reversal symmetry

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.