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

TL;DR

This paper introduces a comprehensive tight-binding model for rhombohedral topological insulators that accurately describes bulk and surface states across the entire Brillouin zone, including effects of symmetry breaking and external fields.

Contribution

The paper presents a novel tight-binding model capturing the full Brillouin zone band structure and topological surface states of rhombohedral topological insulators, incorporating symmetry breaking effects.

Findings

Model accurately describes bulk band structure and surface Dirac cones.

Symmetry breaking influences orbital hybridization and band mixing.

Strategies like stacking faults and electric fields can shift bulk states away from the Dirac point.

Abstract

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.