Valley pseudospin in monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$

For a long time, two-dimensional (2D) hexagonal ${\mathrm{MoS}}_2$ was proposed as a promising material for the valleytronic system. However, the limited size of growth and low carrier mobility in ${\mathrm{MoS}}_2$ restrict its further application. Very recently, a new kind of hexagonal 2D MXene, $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$, was successfully synthesized with large size, excellent ambient stability, and considerable hole mobility. In this paper, based on first-principles calculations, we predict that the valley-contrasting properties can be realized in monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and its derivative $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$. Beyond the traditional two-level valleys, the valleys in monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$ are multiple folded, implying another valley dimension. Such multiple-folded valleys can be described by a three-band low-power Hamiltonian. This study presents the theoretical advance and the potential applications of monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$ in valleytronic devices, especially multiple information processing.

Figure 1

(a) Top- and side-view atomic structures of monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$. The shadow demonstrates the unit cell. Phonon spectra for (b) monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and (c) $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$.

Figure 2

Top valence band and bottom conduction band of (a) monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and (b) $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$ in 3D figures.

Figure 3

Brillouin zone color coded by the degree of circular polarization of excitation from the first occupied valence bands (VB) to the first unoccupied conduction bands (CB) in (a) monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and (b) $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$. (c) Circular polarization from the first occupied valence bands (VB) to the second unoccupied conduction bands (EX) of monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$. The dashed and white hexagons are the first Brillouin zones.

Figure 4

Berry curvature distribution of (a) the first occupied valence band (VB) and (b) the first unoccupied conduction band (CB) in the momentum space in monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$. Berry curvature distribution of (c) the VB, (d) the CB, and (e) the second unoccupied conduction band (EX) in monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$.

Figure 5

Fat band structures along the high-symmetric lines of (a) monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and (b) $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$ with including SOC. Illustrated comparison between (c) traditional valleys and (d) multiple-folded valleys. Circles display the chirality of photons, and arrow length implies the photon energy. Red and blue represents up- and down-spin states, respectively.

Figure 6

Fat band structures along the high-symmetric lines of monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$ including SOC. (a) Projection on Mo states with $l=2$, and $m=\pm 2$. Color represents the angular momentum. (b) Projection on Mo states with $l=2$ and $m=0$. Color represents the weight of projection, respectively. Note that projection on other orbitals is small near the Fermi level at the K and K′ points. (c) $k·p$ band structure near the K point in monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{As}}_4$.