Crystal structure and electronic state in layered 3d$^2$ system VI$_3$

Abstract

As a layered 3d$^2$ magnetic material, VI$_3$ possesses competing crystal structures and complex electronic states, which has recently sparked considerable interest. The bulk and monolayer VI$_3$ in the $C2/m$, $C2/c$, $R\bar{3}$ and $P\bar{3}1c$ crystal structures were examined systemically in this article, as were the electronic states in the octahedral local coordinate system using the maximally localized Wannier functions. The results indicate that the ground state of VI$_3$ is a semiconductor in the $C2/c$ structure, and meta-stable half-metallic states can be found in the high-symmetry crystal structure. Further analysis indicates that the Fermi level crosses the t$_{2g}$ band in half-metallic states, while a low-energy occupied bonding state and a high-energy empty anti-bonding state appear in semiconducting states because of I-p$_{\pi}$ and V-t$_{2g}$ hybridization, resulting in a decrease in total energy and the formation of an energy gap. According to the on-site energy, V-t$_{2g}$ is practically three-fold degenerate in the half-metallic state but splits into two groups in the semiconducting state, including two-fold and singlet states. Moreover, it was found that the degeneracy of the low-symmetry structure would be destroyed, allowing the semiconducting state to be easily achieved. Considering the ongoing debate about the structure and electronic state of VI$_3$, it also serves as a starting point for the further study.