Nonlinear Optical Response of Polar Semiconductors in the Terahertz Range

Using the Berry-phase finite-field method, we compute from first-principles the recently measured\footnote{ T. Dekorsy, V. A. Yakovlev, W. Seidel, M. Helm, and F. Keilmann, Phys. Rev. Lett. {\bfseries 90}, 055508 (2003).} infrared (IR) dispersion of the nonlinear susceptibility $\chi^{(2)}$ in III-V zincblende semiconductors. At far-IR (terahertz) frequencies, in addition to the purely electronic response $\chi^{(2)}_{\infty}$, the total $\chi^{(2)}$ depends on three other parameters, $C_1$, $C_2$, and $C_3$, describing the contributions from ionic motion. They relate to the TO Raman polarizability and the second-order displacement-induced dielectric polarization and forces, respectively. Contrary to a widely-accepted model,\footnote{C. Flytzanis, Phys. Rev. B {\bf 6}, 1264 (1972).} but in agreement with the recent experiments on GaAs,$^1$ we find that the contribution from mechanical anharmonicity dominates over electrical anharmonicity. By using Richardson extrapolation to evaluate the Berry's phase in $k$-space by finite differences, we are able to improve the convergence of the nonlinear susceptibility from the usual\footnote{P. Umari and A. Pasquarello, Phys. Rev. B {\bf 68}, 085114 (2003).} ${\cal O}[(\Delta k)^2]$ to ${\cal O}[(\Delta k)^4]$, dramatically reducing the computational cost.