Large second-harmonic generation and linear electro-optic effect in the bulk kagome lattice compound Nb3MX7 (M=Se,S,Te; X=I,Br)

Layered $\mathrm{N}{\mathrm{b}}_{3}M{X}_{7}$ ($M=\mathrm{Se},\mathrm{S},\mathrm{Te}$; $X=\mathrm{I},\mathrm{Br}$) compounds with a noncentrosymmetric kagome lattice structure constitute a promising candidate for exhibiting optical anisotropy and nonlinearity. Nevertheless, there has been limited research on their nonlinear optical properties both theoretically and experimentally. In this paper, we systematically study the linear and nonlinear optical responses of the bulk $\mathrm{N}{\mathrm{b}}_{3}M{X}_{7}$ ($M=\mathrm{Se},\mathrm{S},\mathrm{Te}$; $X=\mathrm{I},\mathrm{Br}$) family. Previously, two distinct stacking sequences (i.e., AA and AB stacking) in $\mathrm{N}{\mathrm{b}}_{3}M{X}_{7}$ compounds had been identified in experiments. Therefore, the influence of the stacking sequence and the isoelectronic substitution on the linear and nonlinear optical response of the $\mathrm{N}{\mathrm{b}}_{3}M{X}_{7}$ compounds are investigated. It reveals that all four materials (AB-$\mathrm{N}{\mathrm{b}}_{3}\mathrm{Te}{\mathrm{I}}_{7}$, AA-$\mathrm{N}{\mathrm{b}}_{3}\mathrm{Te}{\mathrm{I}}_{7}$, AB-$\mathrm{N}{\mathrm{b}}_{3}\mathrm{Se}{\mathrm{I}}_{7}$, and AA-$\mathrm{N}{\mathrm{b}}_{3}\mathrm{SB}{\mathrm{r}}_{7}$) exhibit significant second-harmonic generation and linear electro-optic effects. Notably, the second-harmonic generation coefficient (${\ensuremath{\chi}}_{zzz}^{(2)}$) of AB-$\mathrm{N}{\mathrm{b}}_{3}\mathrm{Te}{\mathrm{I}}_{7}$ reaches 3081 pm/V at 0.91 eV, which is nearly 14 times as large as that of the known nonlinear optical material GaN. Furthermore, AB-$\mathrm{N}{\mathrm{b}}_{3}\mathrm{Te}{\mathrm{I}}_{7}$ exhibits a large linear electro-optic coefficient ${r}_{zzz}$(0) of 5.94 pm/V, which outperforms that of GaN by almost tenfold. The prominent nonlinear optical responses observed in the $\mathrm{N}{\mathrm{b}}_{3}M{X}_{7}$ compounds are attributed to the intralayer directional covalent bonding. Our findings indicate that the $\mathrm{N}{\mathrm{b}}_{3}M{X}_{7}$ materials would have potential applications in nonlinear optical and linear electro-optic devices.