Structural, electrical, and Rashba properties of monolayer Janus ${\mathrm{Si}}_{2}XY$ ($X,Y$ =P, As, Sb, and Bi)

In this paper, the structural, electrical, and spin properties of Janus ${\mathrm{Si}}_{2}XY$ ($X,Y=\text{P}$, As, Sb, Bi) structures are studied using first-principles calculations. Elastic constants and phonon dispersion prove that all these structures are stable. The band structures of six compounds are studied and the electrical properties are compared. The charge density has been studied to discover the charge distribution in the conduction and valence bands. These compounds exhibit Rashba spin splitting at the $\mathrm{\Gamma }$ and $M$ valleys in the conduction band. Biaxial in-plane strain is used to control the electrical and spin properties. The conduction band minimum can be tuned between the $\mathrm{\Gamma }, K$, and $M$ valleys by applying strain. The Rashba spin splitting around the $\mathrm{\Gamma }$ and $M$ valleys in the conduction bands of these structures can be improved by strain and have the potential for applications in spintronic devices.

Figure 1

Janus ${\mathrm{Si}}_{2}XY$ monolayer from the (a) top and (b) side views. The Si, $X$, and $Y$ atoms are indicated by blue, red, and green colors, respectively.

Figure 2

Phonon dispersion for six ${\mathrm{Si}}_{2}XY$ compounds.

Figure 3

The band structures of the stable ${\mathrm{Si}}_{2}XY$.

Figure 4

The charge density distribution of the conduction band at the $\mathrm{\Gamma }$ and $M$ valleys for ${\mathrm{Si}}_2\mathrm{P}\mathrm{As}, {\mathrm{Si}}_2\mathrm{P}\mathrm{Sb}, {\mathrm{Si}}_2\mathrm{As}\mathrm{Sb}$, and ${\mathrm{Si}}_2\mathrm{Sb}\mathrm{Bi}$. The side and top views are plotted for a better understanding. The blue, green, and red colors are used for Si, and lighter and heavier group-V atoms, respectively.

Figure 5

The charge density distribution of the valence band for ${\mathrm{Si}}_2\mathrm{P}\mathrm{As}, {\mathrm{Si}}_2\mathrm{P}\mathrm{Sb}, {\mathrm{Si}}_2\mathrm{As}\mathrm{Sb}$, and ${\mathrm{Si}}_2\mathrm{Sb}\mathrm{Bi}$. The side and top views are plotted for a better understanding. The blue, green, and red colors are used for Si, and lighter and heavier group-V atoms, respectively.

Figure 6

The energy of the $M, K$, and $\mathrm{\Gamma }$ points in the conduction and valence bands as a function of strain.

Figure 7

The band gap of ${\mathrm{Si}}_2\mathrm{P}\mathrm{As}, {\mathrm{Si}}_2\mathrm{P}\mathrm{Sb}, {\mathrm{Si}}_2\mathrm{As}\mathrm{Sb}$, and ${\mathrm{Si}}_2\mathrm{Sb}\mathrm{Bi}$ as a function of strain.

Figure 8

The Rashba coefficient as a function of strain at the $\mathrm{\Gamma }$ and $M$ valleys.