High-order harmonic generation in three-dimensional Weyl semimetals with broken time-reversal symmetry

Abstract

In this paper the nonlinear interaction of a Weyl semimetal (WSM) with a strong driving electromagnetic wave field is investigated. In the scope of the structure-gauge-invariant low-energy nonlinear electrodynamic theory, the polarization-resolved high-order harmonic generation spectra in the WSM with broken time-reversal symmetry are analyzed. The results obtained show that the spectra in the WSM are completely different compared to the two-dimensional graphene case. In particular, at the noncollinear arrangement of the electric and Weyl node momentum separation vectors, anomalous harmonics are generated which are polarized perpendicular to the pump wave electric field. The intensities of anomalous harmonics are quadratically dependent on the momentum space separation of the Weyl nodes. If the right and the left Weyl fermions are merged, we have a four-component trivial massless Dirac fermion and, as a consequence, the anomalous harmonics vanish. In contrast to the anomalous harmonics, the intensities of normal harmonics do not depend on the Weyl nodes' momentum separation vector and the harmonics spectra resemble the picture for a massless three-dimensional Dirac fermion.