We explore anomalous high-harmonic generation in a model that realizes a transition from a broken time-reversal symmetry Weyl semimetal to a semi-Dirac regime, i.e., a gapless semimetal with dispersion that is parabolic in one direction and conical in the other two. We point out the intensity of the induced anomalous high harmonics is high in the semi-Dirac regime. For Weyl semimetals, we reveal anomalous high harmonics are due to excitations at momenta where the dispersion is not strictly linear and that in the linearized low-energy theory the anomalous response is harmonic only. Our findings aid in the experimental characterizations of Weyl, Dirac, and semi-Dirac semimetals.

• Received 19 September 2023
• Revised 19 February 2024
• Accepted 19 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.205130