Correlation between topological band character and chemical bonding in a Bi(14)Rh(3)I(9)-based family of insulators

Recently the presence of topologically protected edge-states in Bi(14)Rh(3)I(9) 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 Bi(14)Rh(3)I(9) 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 Bi(14)Rh(3)I(9) and graphene in terms of [Image: see text]-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 [Image: see text]-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 [Image: see text]-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.