Crystal-momentum-resolved contributions to multiple plateaus of high-order harmonic generation from band-gap materials

We study the crystal-momentum-resolved contributions to the high-order harmonic generation (HHG) in band-gap materials, and identify the relevant initial crystal momenta for the first and higher plateaus of the HHG spectra. We do so by using a time-dependent density-functional theory model of one-dimensional linear chains. We introduce a self-consistent periodic treatment for the infinitely extended limit of the linear chain model, which provides a convenient way to simulate and discuss the HHG from a perfect crystal beyond the single-active-electron approximation. The multiplateau spectral feature is elucidated by a semiclassical $k$-space trajectory analysis with multiple conduction bands taken into account. In the considered laser-interaction regime, the multiple plateaus beyond the first cutoff are found to stem mainly from electrons with initial crystal momenta away from the $\mathrm{\ensuremath{\Gamma}}$ point ($k=0$), while electrons with initial crystal momenta located around the $\mathrm{\ensuremath{\Gamma}}$ point are responsible for the harmonics in the first plateau. We also show that similar findings can be obtained from calculations using a sufficiently large finite model, which proves to mimic the corresponding infinite periodic limit in terms of the band structures and the HHG spectra.