Josephson junctions of Weyl and multi-Weyl semimetals

TL;DR

This paper investigates the Josephson effect in Weyl and multi-Weyl semimetal junctions, revealing a universal critical current resistance product linked to topological winding number changes and analyzing the impact of barrier properties on Josephson phenomena.

Contribution

It provides an analytical expression for Andreev bound states in Weyl semimetal junctions and demonstrates the topological origin of the universal $I_c R_N$ value, also exploring AC Josephson effects and experimental implications.

Findings

Universal $I_c R_N$ value independent of barrier potential.

Change in topological winding number affects Josephson properties.

Barrier thickness influences the Josephson current and Shapiro steps.

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 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.