Structure gauges and laser gauges for the semiconductor Bloch equations in high-order harmonic generation in solids
Structure gauges and laser gauges for the semiconductor Bloch equations in high-order harmonic generation in solids
复制标题
DOI：
10.1103/physreva.101.053411
复制
发表时间：
2020-03
影响因子：
2.9
通讯作者：
L. Yue;M. Gaarde
中科院分区：
文献类型：
--
作者：
L. Yue;M. Gaarde
半导体布洛赫方程（SBEs）通常用于模拟凝聚态中强场激光与物质的相互作用。在没有反转或时间反转对称性的系统中，贝里连接和跃迁偶极相（TDPs）必须包含在sbe中，这反过来又需要为布洛赫态构建一个平滑和周期性的结构规范。在这里，我们说明了拓扑平凡系统的这种结构规范构造的一般方法。此外，我们还研究了长度计和速度计中的sbe，并讨论了它们各自在高谐波产生过程中的优点和缺点。我们发现，在我们需要将电流减相或分离为带间和带内贡献的情况下，长度计sbe在计算上更有效。在没有消相和只需要总电流的计算中，速度计sbe与结构计无关，计算效率更高。我们采用两个系统作为数值例子来突出我们的发现：ZnO的一维模型和二维单层六方氮化硼（hBN）。hBN的SBEs中Berry连接或tdp的遗漏导致非物理HHG光谱。当前工作中对结构和激光测量的考虑并不局限于HHG过程，而且适用于所有用sbe进行的强场物质模拟。
The semiconductor Bloch equations (SBEs) are routinely used for simulations of strong-field laser-matter interactions in condensed matter. In systems without inversion or time-reversal symmetries, the Berry connections and transition dipole phases (TDPs) must be included in the SBEs, which in turn requires the construction of a smooth and periodic structure gauge for the Bloch states. Here, we illustrate a general approach for such a structure-gauge construction for topologically trivial systems. Furthermore, we investigate the SBEs in the length and velocity gauges and discuss their respective advantages and shortcomings for the high-harmonic generation (HHG) process. We find that in cases where we require dephasing or separation of the currents into interband and intraband contributions, the length-gauge SBEs are computationally more efficient. In calculations without dephasing and where only the total current is needed, the velocity-gauge SBEs are structure-gauge independent and are computationally more efficient. We employ two systems as numerical examples to highlight our findings: a one-dimensional model of ZnO and the two-dimensional monolayer hexagonal boron nitride (hBN). The omittance of Berry connections or TDPs in the SBEs for hBN results in nonphysical HHG spectra. The structure- and laser-gauge considerations in the current work are not restricted to the HHG process and are applicable to all strong-field matter simulations with SBEs.