Semiperturbative strong-field approximation model for high-harmonic generation from crystals

The strong-field approximation (SFA) model proposed originally for a gaseous phase has been extended to explain the high-harmonic generation (HHG) in solids. In most of the previous works using the SFA model, only two bands near the Fermi energy are included. From another viewpoint, the form of the SFA model is similar to the first-order perturbation expansion with respect to the Rabi frequency, which triggered us to explore whether a higher-order expansion can work. In this paper, we extend the semiperturbative expansion to multiband electron dynamics in solids. We employ higher-order expansions to include more complex electron transition paths involving more than two bands. The high-harmonic spectrum from each perturbative order describes a different electron transition pathway and is verified by comparing with the numerical solution of one-dimensional semiconductor Bloch equations. Our extended approach, which is called the semiperturbation model, offers the distinct advantage for distinguishing contributions to HHG from various transition channels.