Full Brillouin zone, multi-band reconstruction of the electronic structure from high-harmonic spectra

While the all-optical characterization of electronic band structure has been touted as an exciting application of the solid-state high harmonic generation, the practical realization of the idea proves difficult, and neither the full potential nor the limitation of the approach are properly understood. This work demonstrates that a few suitably chosen high-harmonic spectra excited by a single quasi-monochromatic mid-infrared pulse provide sufficient information for a three-dimensional reconstruction of multiple electronic bands extending over the entire Brillouin zone. As a by-product of the surrogate-Hamiltonian approach introduced in this work, individual band-structure components such as transition dipole moments and Berry curvatures can also be obtained.