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

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%. (MIV = 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 D3H1 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.