We study the low-frequency properties of the bulk photovoltaic effect in topological semimetals. The bulk photovoltaic effect is a nonlinear optical effect that generates dc photocurrents under uniform irradiation, which is allowed by noncentrosymmetry. It is a promising mechanism for a terahertz photodetection based on topological semimetals. Here, we systematically investigate the low-frequency behavior of the second-order optical conductivity in point-node semimetals. Through symmetry and power-counting analysis, we show that Dirac and Weyl points with tilted cones show the leading low-frequency divergence. In particular, we find new divergent behaviors of the conductivity of Dirac and Weyl points under circularly polarized light, where the conductivity scales as ${\omega }^{-2}$ and ${\omega }^{-1}$ near the gap-closing point in two and three dimensions, respectively. We provide a further perspective on the low-frequency bulk photovoltaic effect by revealing the complete quantum geometric meaning of the second-order optical conductivity tensor. The bulk photovoltaic effect has two origins, which are the transition of electron position and the transition of electron velocity during the optical excitation, and the resulting photocurrents are, respectively, called the shift current and the injection current. Based on an analysis of two-band models, we show that the injection current is controlled by the quantum metric and Berry curvature, whereas the shift current is governed by the Christoffel symbols near the gap-closing points in semimetals. Finally, for further demonstrations of our theory beyond simple two-band models, we perform first-principles calculations on the shift and injection photocurrent conductivities as well as geometric quantities of antiferromagnetic ${\mathrm{MnGeO}}_3$ and ferromagnetic PrGeAl, respectively, as representatives of real magnetic Dirac and Weyl semimetals. Our calculations reveal gigantic peaks in many nonvanishing elements of photoconductivity tensors below a photon energy of about 0.2 eV in both ${\mathrm{MnGeO}}_3$ and PrGeAl. In particular, we show the ${\omega }^{-1}$ enhancement of the shift conductivity tensors due to the divergent behavior of the geometric quantities near the Dirac and Weyl points as well as slightly gapped topological nodes. Moreover, the low-frequency bulk photovoltaic effect is tunable by carrier doping and magnetization orientation rotation. Our work brings new insights into the structure of nonlinear optical responses as well as the design of semimetal-based terahertz photodetectors.

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拓扑半金属中大体积光伏效应的低频发散和量子几何

我们研究了拓扑半金属中整体光伏效应的低频特性。整体光伏效应是一种非线性光学效应，它在非中心对称性允许的情况下，在均匀照射下产生直流光电流。对于基于拓扑半金属的太赫兹光电检测，这是一种很有前途的机制。在这里，我们系统地研究了点节点半金属中二阶光导率的低频行为。通过对称性和功率计数分析，我们显示了倾斜锥的Dirac和Weyl点显示出领先的低频发散。特别是，我们发现圆偏振光下Dirac和Weyl点的电导率有新的发散行为，其中电导率按比例缩放${\omega }^{-2}$ 和 ${\omega }^{-\mathrm{1个}}$分别在二维和三维上接近间隙闭合点。通过揭示二阶光导张量的完整量子几何含义，我们提供了关于低频整体光伏效应的进一步观点。整体光伏效应有两个起源，分别是光激发过程中电子位置的转变和电子速度的转变，所产生的光电流分别称为移位电流和注入电流。基于对两个频带模型的分析，我们表明注入电流受量子度量和Berry曲率控制，而偏移电流受半金属中间隙闭合点附近的Christoffel符号控制。最后，除了简单的两波段模型以外，为了进一步证明我们的理论，${\mathrm{锰锗}}_3$和铁磁PrGeAl分别代表真正的磁性Dirac和Weyl半金属。我们的计算结果表明，在两种情况下，光导张量的许多不消失元素中的巨峰都低于约0.2 eV的光子能量${\mathrm{锰锗}}_3$和PrGeAl。特别是，我们展示了${\omega }^{-\mathrm{1个}}$由于Dirac和Weyl点附近的几何量以及略微间隔的拓扑结点的发散行为，提高了位移电导张量。而且，低频整体光伏效应可通过载流子掺杂和磁化取向旋转来调节。我们的工作为非线性光学响应的​​结构以及基于半金属的太赫兹光电探测器的设计带来了新的见解。