Nonperturbative topological current in Weyl and Dirac semimetals in laser fields

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 epsilon* = mu omega/2evF (omega, laser frequency; mu, Fermi energy; v(F), Fermi velocity). In the perturbative regime, the anomalous Hall current depends quadratically on the field strength (epsilon), 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 (ln epsilon)/epsilon, 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.