Multi-Weyl semimetals are new types of topological semimetals whose topological charge is equal to the value of the winding number J. Here, we investigate the single-particle ballistic scattering on a rectangular barrier in multi-Weyl semimetals. Because this system has a crystallographic anisotropy, the scattering properties depend on the mutual orientation of the crystalline axis and the barrier. For different J, the vertical component of the wave vector k 1 and the corresponding probability current density j(perpendicular to) satisfies j(perpendicular to) proportional to k(perpendicular to)(2J-1). In the case of a barrier perpendicular to the z-axis, it is found that the reflectionless incident angles are determined by geometrical resonances between the barrier width and the de Broglie length of the scattered electrons in the barrier region. In the z-axis direction, the local minimum conductance G(min) occurs when the chemical potential equals the barrier height and G(min) proportional to 1/L-2/J, where L is the width of the barrier. Differently, in the case of a barrier perpendicular to the x-axis, the angular distribution of the transmission probability is no longer rotation invariant. For the double-Weyl semimetals (J = 2), the transmission probability decreases rapidly to 0 as the barrier width L increases for a normal incidence, which is similar to conventional nonrelativistic electrons. It is interesting that perfect transmission is again found for normally incident Weyl fermions for the triple-Weyl semimetals (J = 3). In this case, the tunneling indicates a property similar to that in the case of J = 1.
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