Josephson junctions of Weyl and multi-Weyl semimetals
K. V. Kulikov, Debabrata Sinha, Yu. M. Shukrinov, K. Sengupta
Abstract
We study a Josephson junction involving a Weyl and a multi-Weyl semimetal separated by a barrier region of width $d$ created by putting a gate voltage ${U}_{0}$ over the Weyl semimetal. The topological winding number of such a junction changes across the barrier. We show that ${I}_{c}{R}_{N}$ for such junctions, where ${I}_{c}$ is the critical current and ${R}_{N}$ the normal-state resistance, in the thin-barrier limit, has a universal value independent of the barrier potential. We provide an analytical expression of the Andreev bound states and use it to demonstrate that the universal value of ${I}_{c}{R}_{N}$ is a consequence of change in topological winding number across the junction. We also study the AC Josephson effect in such a junction in the presence of an external microwave radiation, chart out its current-voltage characteristics, and show that the change in the winding number across the junction shapes the properties of its Shapiro steps. We discuss the effect of increasing barrier thickness $d$ on the above-mentioned properties and chart-out experiments which may test our theory.