Layers and phase identification of h- and m-GaTe via second harmonic generation

Two-dimensional (2D) GaTe is a recently synthesized III-VI semiconductor that can crystallize in either a hexagonal (h) phase or a monoclinic (m) phase, and these two phases show clearly different electronic and optical anisotropies. For reliable device fabrication it is very useful to have a fast, non-destructive and low-cost method that can identify both the phase and the layer number of multilayer GaTe over a large area, but such a method has not been fully established. In this work we use first-principles calculations at both the PBE and HSE06 levels to compare, in a uniform way, the structural stability, electronic structures, linear optical responses and second-harmonic generation (SHG) properties of h- and m-GaTe from the monolayer to the pentlayer. The band gaps of the two phases decrease gradually when the layer number increases, and for five layers the band gaps are already very close to the corresponding bulk values. The evolution of symmetry is however very different. All multilayer m-GaTe and all even-layer h-GaTe are centrosymmetric, therefore their SHG responses vanish. Odd-layer h-GaTe is non-centrosymmetric and gives a strong SHG signal. The monolayer h-GaTe shows a peak SHG susceptibility of 529.30 pm V^-1 at 2.15 eV, the trilayer and the pentlayer still reach 114.42 pm V^-1 and 69.76 pm V^-1, and these values are higher than many typical bulk nonlinear crystals calculated within the same scheme. Although the band gap becomes smaller for thicker structures, the main SHG peak of odd-layer h-GaTe does not show a clear red shift. A k-resolved analysis indicates that the dominant contribution comes from interband transitions that are localized near high-symmetry k points and not from simple band-edge transitions, which explains the nearly fixed SHG peak position. Polarization- and angle-resolved SHG patterns of odd-layer h-GaTe show a pronounced sixfold feature, so the crystal orientation can be identified directly. These results confirm that SHG can serve as a robust optical fingerprint that distinguishes h-GaTe from m-GaTe and that also distinguishes odd-layer h-GaTe from even-layer h-GaTe, and the method is fast, non-destructive and suitable for large-area inspection.