A tight-binding model for the band dispersion in rhombohedral topological insulators over the whole Brilluoin zone

We put forward a tight-binding model for rhombohedral topological insulators materials with the space group $D^{5}_{3d}(R\bar{3}m)$. The model describes the bulk band structure of these materials over the whole Brillouin zone. Within this framework, we also describe the topological nature of surface states, characterized by a Dirac cone-like dispersion and the emergence of surface projected bulk states near to the Dirac-point in energy. We find that the breaking of the $R_{3}$ symmetry as one moves away from the $\Gamma$ point has an important role in the hybridization of the $p_x$, $p_y$, and $p_z$ atomic orbitals. In our tight-binding model, the latter leads to a band mixing matrix element ruled by a single parameter. We show that our model gives a good description of the strategies/mechanisms proposed in the literature to eliminate and/or energy shift the bulk states away from the Dirac point, such as stacking faults and the introduction of an external applied electric field.