Electronic structure of zaykovite Rh${}_3$Se${}_4$, prediction and analysis of physical properties of related materials: Pd${}_3$Se${}_4$, Ir${}_3$Se${}_4$, and Pt${}_3$Se${}_4$

In this work, we explore the electronic properties and chemical bonding in the recently discovered mineral zaykovite, the first natural rhodium selenide Rh${}_3$Se${}_4$. We comprehensively studied the bulk electronic structure, hybridization of rhodium and selenium orbitals, and the influence of spin-orbit interaction on the electronic spectrum, as well as inspected its topological properties. Besides, we investigated the surface electronic structure of zaykovite and revealed the anisotropic Rashba-type spin splitting in the surface states. In addition, using calculations of the phonon spectra and enthalpy of formation we predicted the family of similar selenides based on other $4d$ and $5d$ transition metals such as Ir, Pd, and Pt. The structural and electronic properties of these materials are discussed.