Correlation between topological band character and chemical bonding in a $\mathbf{Bi_{14}Rh_{3}I_{9}}$-based family of insulators

TL;DR

This study investigates a family of topological insulators derived from Bi$_{14}$Rh$_3$I$_9$ by substituting different transition metals, revealing how chemical bonding influences their topological properties through density functional theory and tight-binding models.

Contribution

It introduces a unified analysis of the entire family of TIs, linking the topological character to the $d$-band position and chemical bonding within the layers.

Findings

Topologically non-trivial gaps in Ir-, Rh-, Pt-, Pd-based systems.

Os- and Ru-based systems remain topologically trivial.

The $d$-band center position correlates with the topological phase.

Abstract

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 $p_z$-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.