Protected valley states and generation of valley- and spin-polarized current in monolayer ${MA}_2{Z}_4$

The optical selection rules obeyed by two-dimensional materials with spin-valley coupling enable the selective excitation of carriers. We show that several members of the monolayer ${MA}_2{Z}_4$ ($M=\mathrm{Mo}$ and $W;A=\mathrm{C}$, Si, and Ge; $Z=\mathrm{N}$, P, and As) family are direct band-gap semiconductors with protected valley states and that circularly polarized infrared light can induce valley-selective interband transitions. Therefore, they are able to generate a close to 100% valley- and spin-polarized current under an in-plane bias and circularly polarized infrared light, which can be exploited to encode, process, and store information.

Figure 1

(a) Top and (b) side views of the relaxed structure of ${MA}_2{Z}_4$. The blue, red, and green balls represent the $M, A$, and $Z$ atoms, respectively. The unit cell is marked by dashed lines in (a). The structure can be regarded as an ${MZ}_2$ triple layer [resembling 1H-phase ${\mathrm{MoS}}_2$; dashed rectangle in (b)] encapsulated by buckled $AZ$ layers.

Figure 2

(a)-(i) Band structures of monolayer ${MoA}_2{Z}_4$. The direct band-gap materials are shaded orange.

Figure 3

(a)-(i) Band structures of monolayer ${\mathrm{W}A}_2{X}_4$. The direct band gap materials are shaded orange.

Figure 4

Band structures of monolayer ${\mathrm{MoSi}}_2{\mathrm{P}}_4, {\mathrm{MoSi}}_2{\mathrm{As}}_4, {\mathrm{WSi}}_2{\mathrm{P}}_4, {\mathrm{WSi}}_2{\mathrm{As}}_4, {\mathrm{WGe}}_2{\mathrm{P}}_4$, and ${\mathrm{WGe}}_2{\mathrm{As}}_4$. Red (blue) represents dominance of the spin-up (spin-down) component.

Figure 5

(a) Schematic of the valleys near the $K$ and $K^{\prime }$-points, (b) charge densities at the VBM and CBM of ${\mathrm{MoSi}}_2{\mathrm{P}}_4$, (c) band structure of 1H-phase ${\mathrm{MoP}}_2$, (d) partial densities of states (PDOSs) of ${\mathrm{MoSi}}_2{\mathrm{P}}_4$, (e) orbital-projected band structure of ${\mathrm{MoSi}}_2{\mathrm{P}}_4$, and (f) Berry curvature of ${\mathrm{MoSi}}_2{\mathrm{P}}_4$.

Figure 6

(a) Schematic of the monolayer ${MA}_2{Z}_4$ device, (b) schematic of the generation of valley-polarized current, (c) valley components of the normalized current, (d) valley polarization, (e) spin components of the normalized current, and (f) spin polarization.

Figure 7

(a) Valley components of the normalized current, (b) spin components of the normalized current, (c) valley polarization, and (d) spin polarization of the monolayer ${\mathrm{MoSi}}_2{\mathrm{P}}_4, {\mathrm{MoSi}}_2{\mathrm{As}}_4, {\mathrm{WSi}}_2{\mathrm{P}}_4, {\mathrm{WSi}}_2{\mathrm{As}}_4, {\mathrm{WGe}}_2{\mathrm{P}}_4$, and ${\mathrm{WGe}}_2{\mathrm{As}}_4$ devices at $V_{\mathrm{DS}}=0.1\mathrm{V}$.