Transport across junctions of a Weyl and a multi-Weyl semimetal

We study transport across junctions of a Weyl and a multi-Weyl semimetal (WSM and a MSM) separated by a region of thickness $d$ which has a barrier potential $U_0$. We show that in the thin barrier limit ($U_0 \to \infty$ and $d \to 0$ with $\chi=U_0 d/(\hbar v_F)$ kept finite, where $v_F$ is velocity of low-energy electrons and $\hbar$ is Planck's constant), the tunneling conductance $G$ across such a junction becomes independent of $\chi$. We demonstrate that such a barrier independence is a consequence of the change in the topological winding number of the Weyl nodes across the junction and point out that it has no analogue in tunneling conductance of either junctions of two-dimensional topological materials (such as graphene or topological insulators) or those made out of WSMs or MSMs with same topological winding numbers. We study this phenomenon both for normal-barrier-normal (NBN) and normal-barrier-superconductor (NBS) junctions involving WSMs and MSMs with arbitrary winding numbers and discuss experiments which can test our theory.