Electron correlation Time-Dependent Density-Functional Theory for Higher Harmonic generation in solids

We present details of our Time-Dependent Density-Functional Theory (TDDFT) approach, which takes into account the effects of electron-electron correlations, to analyze high-order harmonic (HH) spectra in solids. The used TDDFT exchange-correlation kernel was obtained from the charge susceptibility for the effective Hubbard model for the system calculated by using Dynamical Mean-Field Theory. The corresponding system of the TDDFT equations for polarizations and state occupancies is a generalization of the semiconductor Bloch equations on the case of locally-interacting electrons. To establish the signs of the correlation effects in the HH spectrum, we solved the equations analytically in the limit of weak external laser-pulse perturbation and numerically for various field strengths in the case of one of the most studied system – ZnO. It was found that correlation effects significantly affect the HH spectrum, most notably by shifting the spectral weight to higher harmonics. We discuss possible extensions of the theory on the case of non-local electron-electron interactions.