  We investigate the tunneling of the quasiparticles arising in multi-Weyl
semimetals through a barrier consisting of both electrostatic and vector
potentials, existing uniformly in a finite region along the transmission axis.
The dispersion of a multi-Weyl semimetal is linear in one direction (say,
$k_z$), and proportional to $k_\perp^J$ in the plane perpendicular to it (where
$k_\perp =\sqrt{k_x^2+k_y^2}$). Hence, we study the cases when the barrier is
perpendicular to $k_z$ and $k_x$, respectively. For comparison, we also state
the corresponding results for the Weyl semimetal.
