Accurate electronic properties and non-linear optical response of two-dimensional MA2Z4

Abstract

Two-dimensional MA₂Z₄ (M = Mo, W, V, Nb, Ta, Ti, Zr, Hf, or Cr; A = Si or Ge; Z = N, P, or As) is a new lead in the 2D family, because it exhibits versatile properties by tuning the components M, A and Z. However, theoretical studies on MA₂Z₄ are quite limited, and electronic properties are mainly studied by standard DFT levels, which seriously underestimates the band gap. Here, we systematically investigated the electronic properties and nonlinear optical response of MA₂Z₄ using a hybrid HSE06 functional. It was found that replacing component Z changes the lattice constant most, while the lattice influence by component M substitution is only slight. We showed that the gap difference between PBE and HSE06 is generally about 30% but can be up to 101%. (M^IV = Hf, Ti, or Zr)Si₂N₄ possesses multi-valley characteristics. Furthermore, the second-harmonic generation (SHG) responses of various MA₂Z₄ composites were also calculated. Three non-zero elements of second order non-linear susceptibilities are revealed for MA₂Z₄ with the relationship: d₁₆ = d₂₁ = d₂₂, indicating that MA₂Z₄ belongs to the D_3H¹ space group. HfSi₂N₄ possesses a multi-valley characteristic, and exhibits the largest susceptibility under broad wavelengths and the value of d₂₁ reaches 3697.04 pm V⁻¹ at band gap resonance energy. Intriguingly, the non-linear coefficients of MoSi₂P₄ and MoSi₂As₄ in the IR region are two orders of magnitude larger than those of other well-known non-linear crystals, such as LiGaS₂ and BaAl₄S₇. We further explored the anisotropic SHG response by the polar plot of intensity under different incident light into MA₂Z₄. Our work provides theoretical guidelines for further experimental explorations of MA₂Z₄ and paves the way for its utilization in non-linear optic devices.