Long-range Corrected Exchange-Correlation Kernels to Describe Excitons in Second-Harmonic Generation

We investigate the role of excitons in second-harmonic generation (SHG) through the long-range corrected (LRC) exchange-correlation kernels: empirical LRC, Bootstrap, and jellium-with-a-gap model. We calculate the macroscopic second-order frequency-dependent susceptibility χ(2). We also present the frequency-dependent macroscopic dielectric function ϵM which is a fundamental quantity in the theoretical derivation of χ(2). We assess the role of the long-range kernels in describing excitons in materials with different symmetry types: cubic zincblende, hexagonal wurtzite, and tetragonal symmetry. Our studies indicate that excitons play an important role in χ(2) bringing a strong enhancement of the SHG signal. Moreover, we found that the SHG enhancement follows a simple trend determined by the magnitude of the long-range corrected α-parameter. This trend is material dependent.