Novel electronic properties of monoclinic MP4 (M = Cr, Mo, W) compounds with or without topological nodal line

Abstract

Transition metal phosphides hold novel metallic, semimetallic, and semiconducting behaviors. Here we report by ab initio calculations a systematical study on the structural and electronic properties of ${\text{MP}}_4$ (M = Cr, Mo, W) phosphides in monoclinic C2/c ($C_{2h}^6$) symmetry. Their dynamical stabilities have been confirmed by phonon modes calculations. Detailed analysis of the electronic band structures and density of states reveal that ${\text{CrP}}_4$ is a semiconductor with an indirect band gap of 0.47 eV in association with the p orbital of P atoms, while ${\text{MoP}}_4$ is a Dirac semimetal with an isolated nodal point at the $\mathrm{\Gamma }$ point and ${\text{WP}}_4$ is a topological nodal line semimetal with a closed nodal ring inside the first Brillouin zone relative to the d orbital of Mo and W atoms, respectively. Comparison of the phosphides with group VB, VIB and VIIB transition metals shows a trend of change from metallic to semiconducting behavior from ${\text{VB-MP}}_4$ to VIIB-${\text{MP}}_4$ compounds. These results provide a systematical understandings on the distinct electronic properties of these compounds.