标题： Wannier-Bloch 方法在固体高次谐波生成中的局域化研究 显示英文标题

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

摘要： 固体中的高次谐波发射为阿秒科学提供了新的途径。 一方面，它使我们能够研究电子在强激光脉冲驱动下的非线性响应的基本过程，这些电子位于周期性晶体晶格中。 另一方面，它开辟了高效阿秒脉冲生成、新型电子波函数成像以及高次谐波产生（HHG）强度增强的新路径。 与原子气体中已充分理解的HHG现象相比，固体中HHG的一个关键特征是该过程的离域化特性，即从周期性晶格中某一位置电离出的电子可以与其它任何位置重新结合。 在这里，我们基于价带中的局域Wannier波函数和导带中的离域Bloch函数，开发了一个解析模型。 这种Wannier-Bloch方法评估了单个晶格位点对HHG过程的贡献，从而精确解决了固体内谐波发射定位的问题。 我们将此模型应用于研究ZnO晶体中两种不同取向的HHG，分别对应较宽和较窄的价带和导带。 有趣的是，在较窄的带隙情况下，HHG过程显示出显著的定位特性，类似于原子中的谐波生成。 对于所有情况，离域贡献在接近带隙能量时最高。 我们的结果为控制固体晶体中局部化的HHG贡献铺平了道路，这对新兴的阿托纳米科学领域具有难以估量的意义。 显示英文摘要

摘要： Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an electron ionized from one site in the periodic lattice may recombine with any other. Here, we develop an analytic model, based on the localized Wannier wave functions in the valence band and delocalized Bloch functions in the conduction band. This Wannier-Bloch approach assesses the contributions of individual lattice sites to the HHG process, and hence addresses precisely the question of localization of harmonic emission in 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, for narrower 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, with hard to overestimate implications for the emerging area of atto-nanoscience.