Nonlinear Optical Response of Polar Semiconductors in the Terahertz Range

We compute the recently measured \footnote{ T. Dekorsy, V. A. Yakovlev, W. Seidel, M. Helm, and F. Keilmann, Phys. Rev. Lett. {\bfseries 90}, 055508 (2003)} infrared dispersion of the second-order nonlinear susceptibility $\chi^{(2)}$ in zincblende semiconductors from first principles. At infrared frequencies, but above the elastic resonance of the medium, the total $\chi^{(2)}$ depends not only on the purely electronic response $\chi^{(2)}_{\infty}$, but also on three additional parameters: $C_1$, $C_2$, and $C_3$. They relate to the TO Raman tensor, second-order dipole moment, and lattice anharmonicity, respectively. We apply small, finite electric fields and finite ionic displacements along [111], and extract the desired parameters from the forces induced on the atoms and the change in macroscopic polarization. By analyzing the resulting displacements of the Wannier-function centers, we make contact with bond-polarizability models and assess the influence of the cation $d$-electrons.