TY - JOUR
T1 - Wannier-bloch approach to localization in high-harmonics generation in solids
AU - Osika, Edyta N.
AU - Chacón, Alexis
AU - Ortmann, Lisa
AU - Suárez, Noslen
AU - Pérez-Hernández, Jose Antonio
AU - Szafran, Bartlomiej
AU - Ciappina, Marcelo F.
AU - Sols, Fernando
AU - Landsman, Alexandra S.
AU - Lewenstein, Maciej
PY - 2017/5/8
Y1 - 2017/5/8
N2 - 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.
AB - 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.
KW - Condensed matter physics
KW - Optics
KW - Quantum physics
UR - http://www.scopus.com/inward/record.url?scp=85021364308&partnerID=8YFLogxK
U2 - 10.1103/PhysRevX.7.021017
DO - 10.1103/PhysRevX.7.021017
M3 - 文献综述
AN - SCOPUS:85021364308
SN - 2160-3308
VL - 7
JO - Physical Review X
JF - Physical Review X
IS - 2
M1 - 021017
ER -