Microscopic analysis of high harmonic generation in semiconductors with degenerate bands
Microscopic analysis of high harmonic generation in semiconductors with degenerate bands
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DOI：
10.1103/physrevb.103.085201
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发表时间：
2020-12
影响因子：
3.7
通讯作者：
Le Huu Thong;C. Ngo;H. T. Duc;Xiaohong Song;T. Meier
中科院分区：
文献类型：
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作者：
Le Huu Thong;C. Ngo;H. T. Duc;Xiaohong Song;T. Meier
基于多带半导体布洛赫方程，提出并分析了一种能正确描述简并带和带交叉的晶体固体中高次谐波产生的微观方法。众所周知，数值能带结构计算通常提供电子波函数与一个未定的$k$-依赖的相位，其结果在矩阵元素，其中包含任意的$k$-依赖的相位。此外，这种方法通常混合退化带和带的能量差小于在任意的方式为$k$空间中的每个点的数值精度。这些模糊性是有问题的，如果一个考虑的动力学引起的电场，因为矩阵元素的位置运营商涉及一个衍生的波函数关于$k$。当光-物质相互作用用长度规范描述时，通过采用沿场方向沿着光滑的规范变换，解决了Bloch态的任意相位和简并子空间混合问题.通过与速度计计算结果的比较，验证了该方法的有效性。虽然我们在两种规范中获得相同的总体结果，但长度规范是有利的，因为它收敛于较少数量的带，因此需要比速度规范少得多的数值工作。此外，带间和带内贡献之间的独特区别以及因此在长度计中的指导性物理解释是可能的，而在速度计中，这是不清楚的。计算的偏振方向相关的高次谐波光谱与GaAs的实验数据吻合得很好。此外，它表明，在适当的条件下，Berry曲率是主要负责的偶次谐波极化垂直于驱动场。
Based on the multiband semiconductor Bloch equations a microscopic approach to high-harmonic generation in crystalline solids which is able to properly describe degenerate bands and band crossings is presented and analyzed. It is well known that numerical band structure calculations typically provide electronic wave functions with an undetermined $k$-dependent phase which results in matrix elements which contain arbitrary $k$-dependent phases. In addition, such approaches usually mix degenerate bands and bands with an energy difference smaller than the numerical precision in an arbitrary way for each point in $k$ space. These ambiguities are problematic if one considers the dynamics induced by electric fields since the matrix elements of the position operator involve a derivative of the wave functions with respect to $k$. When the light-matter interaction is described in the length gauge, the problem of arbitrary phases and degenerate subspace mixing of Bloch states is solved by adopting a smooth gauge transformation along the field direction. The results obtained within this method are validated by comparing with calculations in the velocity gauge. Although we obtain in both gauges the same overall result, the length gauge is advantageous since it converges with a smaller number of bands and thus requires significantly less numerical effort than the velocity gauge. Also a unique distinction between inter- and intraband contributions and thus an instructive physical interpretation is possible in the length gauge whereas in the velocity gauge this is unclear. The computed polarization-direction-dependent high-harmonic spectra agree well with experimental data reported for GaAs. Furthermore, it is demonstrated that, under proper conditions, the Berry curvature is largely responsible for the even-order harmonics which are polarized perpendicular to the driving field.