Effects of quantum interferences among crystal-momentum-resolved electrons in solid high-order harmonic generation

We theoretically demonstrate the effects of quantum interferences among valence electrons with various initial crystal momenta in the high-order harmonic generation (HHG) in solids. By investigating crystal-momentumdependent harmonics from solids in linearly polarized laser fields, some unique radiation characteristics of the observed overall harmonics are attributed to the consequences of interferences among valence electrons with different crystal momenta. It is shown that the electron pairs with opposite crystal momenta result in the destructive interferences of even-order harmonics for a crystal with the inversion symmetry, which eventually leads to the only odd orders in observed overall harmonic spectra for a semiconductor material because of the complete pairing of all valence electrons. Additionally, each of the harmonic plateaus in the overall multiple-plateau harmonic spectrum is identified to be contributed by the valence electrons within different crystal momentum zones. We also find that the solid-phase HHG in the below-band-gap region is substantially suppressed due to the collective responses of multiple valence electrons. This work sheds light on the essential impacts of interferences among crystal-momentum-resolved electrons on the HHG in solids and is helpful to explore ultrafast coherent processes in condensed matter.