Wannier-bloch approach to localization in high-harmonics generation in solids

Abstract

Emission of high-order harmonics from solids provides a new avenue in attosecond science. On the onehand, it allows us to investigate fundamental processes of the nonlinear response of electrons driven by astrong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficientattosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-orderharmonic-generation (HHG) intensity. A key feature of HHG in a solid (as compared to the wellunderstoodphenomenon of HHG in an atomic gas) is the delocalization of the process, whereby an electronionized from one site in the periodic lattice may recombine in any other. Here, we develop an analyticmodel, based on the localizedWannier wave functions in the valence band and delocalized Bloch functionsin the conduction band. This Wannier-Bloch approach assesses the contributions of individual latticesites to the HHG process and hence precisely addresses the question of localization of harmonic emissionin solids. We apply this model to investigate HHG in a ZnO crystal for two different orientations,corresponding to wider and narrower valence and conduction bands, respectively. Interestingly, fornarrower bands, the HHG process shows significant localization, similar to harmonic generation in atoms.For all cases, the delocalized contributions to HHG emission are highest near the band-gap energy.Our results pave the way to controlling localized contributions to HHG in a solid crystal.