Second harmonic generation of $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$-type layers

The recently discovered two-dimensional (2D) layered semiconductor $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ has aroused great interest due to its unique 2D material characteristics. In this study, we found that differences in the structural details for $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ may lead to differences in the intensity of second harmonic generation (SHG) and its response to strain. Accordingly, SHG can be used as a simple technique to identify the structural details of this system. We further calculated the SHG effects of $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ derivatives and investigated their strain-regulation mechanism, especially including the anomalous SHG responses under strain for $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{P}}_4$ and $\mathrm{Mo}{\mathrm{Ge}}_2{\mathrm{P}}_4$, differing from other known 2D materials. The studies may have forward-looking significance for the research of nonlinear optics and optoelectronics in this novel 2D material system.

Figure 1

Structures of α-$\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ (a) and β-$\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ (b), and the SH polarization ($P$) of layers. The arrow directions of $P$ in the outermost layers are opposite due to the different sites of nitrogen.

Figure 2

PDOS and band-resolved SHG analysis of α-$\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ (a) and β-$\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ (b). Black and red lines represent the contribution of the VE and VH process to the total SHG. Inset is the SHG-weight density projected to each atom. The orbitals vital to SHG are clearly highlighted in the real space.

Figure 3

Relative changes of the SHG coefficient ${\chi }_{111}$ with respect to strain ε from −3% to 3% for $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ (a), $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{P}}_4$ (b) and $\mathrm{Mo}{\mathrm{Ge}}_2{\mathrm{P}}_4$ (c), as compared with ML $\mathrm{Mo}{\mathrm{S}}_2$. Inset in (a) is the partial enlarged view.

Figure 4

Schematic diagram of charge transfer for α-$\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and α-$\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{P}}_4$ from strain ε to −ε (a), and SHG density projection of α-$\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{P}}_4$ when strain ε is −3% and 3% (b).