Layer-independent and layer-dependent nonlinear optical properties of two-dimensional GaX (X = S, Se, Te) nanosheets

Recently researchers have found that the non-resonant second-harmonic generation (SHG) intensity of the GaSe monolayer (ML) is the strongest among all two-dimensional (2D) atomic layered crystals. Here we perform a systematic first-principles study of the SHG coefficient of GaX (X = S, Se, Te) monolayers (MLs) and few-layers. We find that the non-resonant SHG intensity of the GaS ML can be comparable with that of the GaSe ML, while the non-resonant SHG intensity of the GaTe ML is much stronger than that of the GaSe ML. Furthermore, the magnitudes of SHG coefficients of the few-layers exfoliated from bulk ε-GaSe and newly constructed N₁-GaSe crystals are very close to that of the GaSe ML, showing no dependence on the layer number. The magnitude of the SHG coefficient of the trilayer exfoliated from the bulk β-GaSe crystals is around 1/3 of that of the GaSe ML, decreasing rapidly with the layer number. This study indicates that a strong SHG response can be obtained in a wide range of monolayers and few-layers. Moreover, we point out that one can identify the layer number and the stacking sequence of 2D nanosheets by measuring their elastic constants and SHG coefficients.