Origin of layer number dependent linear and nonlinear optical properties of two-dimensional graphene-like SiC

Abstract: We theoretically discuss the physical origin of the dielectric constants [{\epsilon}({\omega})] and second harmonic generation coefficients [{chi}(2)({\omega})] of the ABA-stacked two-dimensional graphene-like silicon carbide (2D-SiC) with the number of layers up to 5. It is found that the intensities of the pronounced peaks of both {\epsilon}({\omega}) and {chi}(2)({\omega}) exhibit a clear layer number dependence. For the light polarization parallel to the 2DSiC plane, the monolayer SiC (ML-SiC) and multilayer SiC (MuL-SiC) have very similar pronounced peak positions of {\epsilon}({\omega}), which are attributed to the {\pi}->{\pi}* and {\sigma}->{\sigma}* transitions. However, for the light polarization perpendicular to the 2D-SiC plane, a characteristic peak is found for the MuL-SiC at about 4.0 eV, except that the allowed {\pi}->{\sigma}* and {\sigma}->{\pi}* transition peaks are found for both ML-SiC and MuL-SiC in the high-energy region (> 8 eV). This characteristic peak is attributed to the interlayer {\pi}->{\pi}* transition which does not exist for the ML-SiC, and at this peak position, the ML-SiC has a weak dark exciton based on the mBJ calculation within the Bethe-Salpeter equation framework. For {chi}(2)({\omega}), the single-particle transition channels based on the three-band terms dominate the second harmonic generation process of both ML-SiC and MuL-SiC and determine the size and sign of {chi}(2)({\omega}). In the ultraviolet visible region, the purely interband motion and intraband motion of electrons competitively determine the size and sign of {chi}(2)({\omega}). For the light polarization perpendicular to the 2D-SiC plane, the intraband motion of electrons modulated more dramatically the interband motion than for that parallel to the 2D-SiC plane.