Tunneling of multi-Weyl semimetals through a potential barrier under the influence of magnetic fields

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, kz), and proportional to kJ? in the plane perpendicular to it (where k?=k2x+k2y???????). Hence, we study the cases when the barrier is perpendicular to kz and kx, respectively. For comparison, we also state the corresponding results for the Weyl semimetal.