Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

TL;DR

This paper develops a semiclassical framework to analyze nonlinear magneto-optical effects in topological Dirac/Weyl semimetals, explaining experimental anisotropies and predicting strong second harmonic responses near Weyl points.

Contribution

It introduces a semiclassical Boltzmann approach incorporating Berry curvature and magnetic moments to describe nonlinear optical responses in topological semimetals, connecting with quantum calculations.

Findings

Captures anisotropic linear conductivity under magnetic field.

Predicts strong second harmonic generation near Weyl points.

Reproduces circular photogalvanic effect via quantum Floquet analysis.

Abstract

We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both Berry curvature and orbital magnetic moment. Applied to Weyl fermions, the semiclassical approach (i) captures the directional anisotropy of linear conductivity under magnetic field as a consequence of an anisotropic $B^2$ contribution, which may explain the low-field regime of recent experiments; (ii) predicts strong second harmonic generation proportional to $B$ that is enhanced as the Fermi energy approaches the Weyl point, leading to large nonlinear Kerr rotation. Moreover, we show that the semiclassical formula for the circular photogalvanic effect arising from the Berry curvature dipole is reproduced by a full quantum calculation using a Floquet approach.