The Pyrite Structure of PdS$_{2}$ and PdSe$_{2}$ Monolayers

There has been a rising interest in two-dimensional (2D) materials due to a range of extraordinary electronic, optical and mechanical properties which are different from their bulk counterparts. The structure, stability and electronic properties of 2D PdS$_{2}$ and PdSe$_{2}$ have been investigated in the past in the well-known hexagonal 1T and 2H structures. However, bulk PdS$_{2}$ and PdSe$_{2}$ are layered compounds with individual rhombohedral pyrite-type monolayers vertically stacked with van-der Waals forces. Using density functional theory simulations, and five different functionals, we compare the energetic stability of 2D PdS$_{2}$ and PdSe$_{2}$ pyrite structure with the 1T and 2H structures. We find that the PdS$_{2}$ is most stable in the pyrite structure, whereas the PdSe$_{2}$ is most stable in the 1T structure with the pyrite structure closely competing in energy. The fundamental band gap of these compounds as a function of the structure, number of layers, the stacking arrangement and in-layer strain has been investigated. The pyrite structures of PdS$_{2}$ and PdSe$_{2}$ are found to be semi-conducting with indirect band gaps, and effective masses comparable to that of monolayer MoS$_{2}$; thus are potential candidates for nano-electronic applications.