Nonperturbative Topological Current in Weyl and Dirac Semimetals in Laser Fields

TL;DR

This paper investigates the non-perturbative anomalous Hall current and high harmonic generation in Weyl and Dirac semimetals under strong laser fields, revealing a topological crossover between regimes and novel nonlinear responses.

Contribution

It introduces a non-perturbative analysis of topological currents in semimetals, uncovering a crossover regime and the topological origin of nonlinear optical responses.

Findings

Identification of a crossover electric field strength $ ext{E}^*$ separating regimes.

Saturation and decay of the Hall current in the non-perturbative regime.

Generation of even-order high harmonics when symmetry is broken.

Abstract

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.