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

机译:Wannier-Bloch在高次谐波产生中的定位方法   固体

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摘要

Emission of high-order harmonics from solids provides a new avenue inattosecond science. On one hand, it allows to investigate fundamental processesof the non-linear response of electrons driven by a strong laser pulse in aperiodic crystal lattice. On the other hand, it opens new paths towardefficient attosecond pulse generation, novel imaging of electronic wavefunctions, and enhancement of high-order harmonic generation (HHG) intensity. Akey feature of HHG in a solid (as compared to the well-understood phenomena ofHHG in an atomic gas) is the delocalization of the process, whereby an electronionized from one site in the periodic lattice may recombine with any other.Here, we develop an analytic model, based on the localized Wannier wavefunctions in the valence band and delocalized Bloch functions in the conductionband. This Wannier-Bloch approach assesses the contributions of individuallattice sites to the HHG process, and hence addresses precisely the question oflocalization of harmonic emission in solids. We apply this model to investigateHHG in a ZnO crystal for two different orientations, corresponding to wider andnarrower valence and conduction bands, respectively. Interestingly, fornarrower bands, the HHG process shows significant localization, similar toharmonic generation in atoms. For all cases, the delocalized contributions toHHG emission are highest near the band-gap energy. Our results pave the way tocontrolling localized contributions to HHG in a solid crystal, with hard tooverestimate implications for the emerging area of atto-nanoscience.
机译:固体中高次谐波的发射提供了一种新的方法,使之成为了亚秒级科学。一方面,它允许研究非周期性晶格中强激光脉冲驱动的电子的非线性响应的基本过程。另一方面,它为高效的阿秒脉冲产生,电子波函数的新颖成像以及增强高次谐波产生(HHG)强度开辟了新的途径。固体中HHG的一个关键特征(与原子气体中HHG众所周知的现象相比)是过程的离域化,即从周期性晶格中一个位置电离的电子可能与其他任何位置复合。解析模型,基于价带中的局部Wannier波函数和导带中的离域Bloch函数。这种Wannier-Bloch方法评估了各个晶格位点对HHG过程的贡献,因此精确地解决了固体中谐波发射的局部化问题。我们应用该模型研究ZnO晶体中HHG的两个不同方向,分别对应于更宽和更窄的价带和导带。有趣的是,更窄的波段,HHG过程显示出显着的局域性,类似于原子中的谐波产生。对于所有情况,在带隙能量附近,对HHG排放的离域贡献最高。我们的研究结果为控制固态晶体中对HHG的局部贡献铺平了道路,而这对于高估纳米科学的新兴领域却难以高估。

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