Nonperturbative Topological Current in Weyl and Dirac Semimetals in Laser Fields

• Published in: arXiv.org 2020-08
• Main Authors: Dantas, Renato M A, Wang, Zhe, Surówka, Piotr, Oka, Takashi
• Format: Article
• Language: English
• Subjects: Boltzmann transport equation; Electric field strength; Exact solutions; Harmonics; Kinetic theory; Lasers; Metalloids; Nonlinear response; Topology
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2008.04331

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 \(\mathcal{E}^{*}= \frac{\mu \omega}{ 2 e v_F}\) (\(\omega\): laser frequency, \(\mu\): 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.