We investigate the influence of a time-periodic driving (for example, by shining circularly polarized light) on three-dimensional Weyl and multi-Weyl semimetals, in the planar Hall and planar thermal Hall set-ups. We incorporate the effects of the drive by using the Floquet formalism in the large frequency limit. We evaluate the longitudinal magneto-conductivity, planar Hall conductivity, longitudinal thermo-electric coefficient, and transverse thermo-electric coefficient, using the semi-classical Boltzmann transport equations. We demonstrate the explicit expressions of these transport coefficients in certain limits of the system parameters, where it is possible to perform the integrals analytically. We cross-check our analytical approximations by comparing the physical values with the numerical results, obtained directly from the numerical integration of the integrals. The answers obtained show that the topological charges of the corresponding semimetals have profound signatures in these transport properties, which can be observed in experiments.

我们研究了平面霍尔和平面热霍尔装置中时间周期驱动（例如，通过照射圆偏振光）对三维外尔和多外尔半金属的影响。我们通过在大频率限制中使用 Floquet 形式来结合驱动的影响。我们使用半经典玻尔兹曼输运方程评估纵向磁导率、平面霍尔电导率、纵向热电系数和横向热电系数。我们在系统参数的某些限制下演示了这些传输系数的显式表达式，其中可以分析地执行积分。我们通过将物理值与数值结果进行比较来交叉检查我们的分析近似值，直接从积分的数值积分中获得。获得的答案表明，相应半金属的拓扑电荷在这些传输特性中具有深刻的特征，这可以在实验中观察到。