论文标题
在激光场中的Weyl和Dirac半法中的非扰动拓扑电流
Nonperturbative Topological Current in Weyl and Dirac Semimetals in Laser Fields
论文作者
论文摘要
我们在动力学理论的背景下，通过强烈的椭圆极化激光场在WEYL和DIRAC半学中产生的异常霍尔电流及其高谐波进行非扰动。我们发现以电场强度$ \ MATHCAL {E}^{*} = \ frac {μΩ} {2 E V_F} $（$ v_f} $（$ω$：激光频率，$μ$：fermi Energy，$ v_f $：fermi velerocity）。在扰动状态下，异常的霍尔电流四次地取决于场强（$ \ Mathcal {e} $），而高阶校正以及高谐波在零温度下消失。在非扰动制度中，异常的霍尔电流饱和，并衰减为$（\ log {\ Mathcal {e}}}）/\ Mathcal {e} $，而当平面旋转对称性损坏时，会生成均匀的高谐波。基于Boltzmann方程的分析解决方案，我们揭示了尖锐跨界的拓扑起源：Weyl Monopole在同性或非替代方案中的虚拟运动中分别在Fermi Sphere内部或在费米球体外部移动。我们的发现建立了一种与拓扑结合的新的非线性响应，该响应与拓扑结构为特征，其特征是Weyl和Dirac Semimetals。
We study non-perturbatively the anomalous Hall current and its high harmonics generated in Weyl and Dirac semimetals by strong elliptically polarized laser fields, in the context of kinetic theory. We find a novel crossover between perturbative and non-perturbative regimes characterized by the electric field strength $\mathcal{E}^{*}= \frac{μω}{ 2 e v_F}$ ($ω$: laser frequency, $μ$: Fermi energy, $v_F$: Fermi velocity). In the perturbative regime, the anomalous Hall current quadratically depends on the field strength ($\mathcal{E}$), whereas the higher order corrections, as well as high harmonics, vanish at zero temperature. In the non-perturbative regime, the anomalous Hall current saturates and decays as $(\log{\mathcal{E}})/\mathcal{E}$, while even-order high harmonics are generated when inplane rotational symmetry is broken. Based on the analytical solution of the Boltzmann equation, we reveal the topological origin of the sharp crossover: the Weyl monopole stays inside or moves outside of the Fermi sphere, respectively, during its fictitious motion in the pertubative or non-pertubative regimes. Our findings establish a new non-linear response intrinsically connected to topology, characteristic to Weyl and Dirac semimetals.
