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Free keywords:
Boltzmann equation, Electric fields, Harmonic analysis, Topology, Electric field strength, Elliptically polarized laser field, Fermi velocities, Laser frequency, Non-linear response, Rotational symmetries, Topological currents, Zero temperatures, Laser theory
Abstract:
We study nonperturbatively 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 crossover between perturbative and nonperturbative regimes characterized by the electric field strength E∗=μω2evF (ω, laser frequency; μ, Fermi energy; vF, Fermi velocity). In the perturbative regime, the anomalous Hall current depends quadratically on the field strength (E), whereas the higher-order corrections, as well as high harmonics, vanish at zero temperature. In the nonperturbative regime, the anomalous Hall current saturates and decays as (lnE)/E, while even-order high harmonics are generated when in-plane 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 perturbative or nonperturbative regimes. Our findings establish a nonlinear response intrinsically connected to topology, characteristic of Weyl and Dirac semimetals. © 2021 authors. Published by the American Physical Society.
