Multivalued current-phase relationship in a.c. Josephson effect for a three-dimensional Weyl semimetal WTe$_2$

TL;DR

This study demonstrates the multivalued current-phase relationship in a WTe$_2$ Weyl semimetal Josephson junction, revealing fractional Shapiro steps and the influence of topological surface states on the a.c. Josephson effect.

Contribution

It provides experimental evidence of fractional Josephson effects in a Weyl semimetal, highlighting the role of topological surface states and contrasting with other topological materials.

Findings

Observation of integer and fractional Shapiro steps.

Absence of 4π periodicity in WTe$_2$ junctions.

Connection of fractional effects to Weyl surface states.

Abstract

We experimentally study electron transport between two superconducting indium leads, coupled to a single WTe$_2$ crystal, which is a three-dimensional Weyl semimetal. We demonstrate Josephson current in long 5~$\mu$m In-WTe$_2$-In junctions, as confirmed by the observation of integer (1,2,3) and fractional (1/3, 1/2, 2/3) Shapiro steps under microwave irradiation. Demonstration of fractional a.c. Josephson effect indicates multivalued character of the current-phase relationship, which we connect with Weyl topological surface states contribution to Josephson current. In contrast to topological insulators and Dirac semimetals, we do not observe $4\pi$ periodicity in a.c. Josephson effect for WTe$_2$ at different frequencies and power, which might reflect chiral character of the Fermi arc surface states in Weyl semimetal.