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, k<inf>z</inf>), and proportional to k<inf>⊥</inf>^J in the plane perpendicular to it (where k<inf>⊥</inf>=k<inf>x</inf>²+k<inf>y</inf>²). Hence, we study the cases when the barrier is perpendicular to k<inf>z</inf> and k<inf>x</inf>, respectively. For comparison, we also state the corresponding results for the Weyl semimetal.