  The successful realization of the topological Weyl semimetals has
revolutionized contemporary physics. In recent years, multi-Weyl semimetals, a
class of topological Weyl semimetals, has attracted broad interest in
condensed-matter physics. Multi-Weyl semimetals are emerging topological
semimetals with nonlinear anisotropic energy dispersion, which is characterized
by higher topological charges. In this study, we investigate how the
topological charge affects the nonlinear optical response from multi-Weyl
semimetals. It has been observed that the laser-driven electronic current is
characteristic of the topological charge, and
  the laser polarization's direction influences the current's direction and
amplitude. In addition, the anomalous current, perpendicular to the laser's
polarization, carries a distinct signature of the topological charges and
encodes the information about the parity and amplitude of the nontrivial Berry
curvature. We show that the anomalous current associated with the anomalous
Hall effect remains no longer proportional to the topological charge at higher
laser intensity -- a significant deviation from the linear response theory.
High-harmonic spectroscopy is employed to capture the distinct and interesting
features of the currents in multi-Weyl semimetals where the topological charge
drastically impacts the harmonics' yield and energy cutoff.
