Valley-dependent properties of monolayer MoSi2N4, WSi2N4, and MoSi2As4

In a recent work, new two-dimensional materials, monolayer ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ and ${\mathrm{WSi}}_{2}{\mathrm{N}}_{4}$, were successfully synthesized in experiment, and several other monolayer materials with a similar structure, such as ${\mathrm{MoSi}}_{2}{\mathrm{As}}_{4}$, were predicted [Hong et al., Science 369, 670 (2020)]. Here, based on first-principles calculations and theoretical analysis, we investigate the electronic and optical properties of monolayer ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}, {\mathrm{WSi}}_{2}{\mathrm{N}}_{4}$, and ${\mathrm{MoSi}}_{2}{\mathrm{As}}_{4}$. We show that these materials are semiconductors, with a pair of Dirac-type valleys located at the corners of the hexagonal Brillouin zone. Due to the broken inversion symmetry and the effect of spin-orbit coupling, the valley fermions manifest spin-valley coupling, valley-contrasting Berry curvature, and valley-selective optical circular dichroism. We also construct the low-energy effective model for the valleys, calculate the spin Hall conductivity and the permittivity, and investigate the strain effect on the band structure. Our result reveals interesting valley physics in monolayer ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}, {\mathrm{WSi}}_{2}{\mathrm{N}}_{4}$, and ${\mathrm{MoSi}}_{2}{\mathrm{As}}_{4}$, suggesting their great potential for valleytronics and spintronics applications.