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

In a recent work, new two-dimensional materials, the monolayer\nMoSi$_{2}$N$_{4}$ and WSi$_{2}$N$_{4}$, have been successfully synthesized in\nexperiment, and several other monolayer materials with the similar structure,\nsuch as MoSi$_{2}$As$_{4}$, have been predicted [{\\color{blue}Science 369,\n670-674 (2020)}]. Here, based on first-principles calculations and theoretical\nanalysis, we investigate the electronic and optical properties of monolayer\nMoSi$_{2}$N$_{4}$, WSi$_{2}$N$_{4}$ and MoSi$_{2}$As$_{4}$. We show that these\nmaterials are semiconductors, with a pair of Dirac-type valleys located at the\ncorners of the hexagonal Brillouin zone. Due to the broken inversion symmetry\nand the effect of spin-orbit coupling, the valley fermions manifest spin-valley\ncoupling, valley-contrasting Berry curvature, and valley-selective optical\ncircular dichroism. We also construct the low-energy effective model for the\nvalleys, calculate the spin Hall conductivity and the permittivity, and\ninvestigate the strain effect on the band structure. Our result reveals\ninteresting valley physics in monolayer MoSi$_{2}$N$_{4}$, WSi$_{2}$N$_{4}$ and\nMoSi$_{2}$As$_{4}$, suggesting their great potential for valleytronics and\nspintronics applications.\n