Correlation between topological band character and chemical bonding in a Bi₁₄Rh₃I₉ - based family of insulators

Recently the presence of topologically protected edge-states in Bi14Rh3I9 was confirmed by scanning tunnelling microscopy consolidating this compound as a weak 3D topological insulator (TI). Here, we present a density-functional-theory-based study on a family of TIs derived from the Bi14Rh3I9 parent structure via substitution of Ru, Pd, Os, Ir and Pt for Rh. Comparative analysis of the band-structures throughout the entire series is done by means of a unified minimalistic tight-binding model that evinces strong similarity between the quantum-spin-Hall (QSH) layer in Bi14Rh3I9 and graphene in terms of p(z) -molecular orbitals. Topologically non-trivial energy gaps are found for the Ir-, Rh-, Pt-and Pd-based systems, whereas the Os-and Ru-systems remain trivial. Furthermore, the energy position of the metal d-band centre is identified as the parameter which governs the evolution of the topological character of the band structure through the whole family of TIs. The d-band position is shown to correlate with the chemical bonding within the QSH layers, thus revealing how the chemical nature of the constituents affects the topological band character