Shapiro Steps as a Direct Probe of $\pm s$-wave Symmetry in Multi-gap Superconducting Josephson Junctions

TL;DR

This paper theoretically investigates how Shapiro steps in hetero Josephson junctions reveal the $ ext{±}s$-wave symmetry of a two-gap superconductor through anomalous current and step height patterns at resonance.

Contribution

It introduces a method to identify $ ext{±}s$-wave symmetry via Shapiro step analysis in Josephson junctions, highlighting the role of Josephson-Leggett mode resonance.

Findings

Anomalous DC Josephson current appears at Josephson-Leggett mode frequency.

Step heights alternate, indicating gap symmetry: enhanced odd steps for $ ext{±}s$-wave, even steps for s-wave.

Fractional Shapiro steps are predicted in the system.

Abstract

We theoretically study the Shapiro steps in a hetero Josephson junction made of a single-gap superconductor and a two-gap one. We find that an anomalous DC Josephson current is induced by tuning the frequency of an applied microwave to the Josephson-Leggett mode frequency, which creates an extra step structure in the $I$-$V$ characteristics besides the conventional Shapiro steps. The step heights at the resonance voltages exhibit an alternate structure of a large and small value reflecting the gap symmetry of the two-gap superconductor. In the $\pm s-wave case in which the two gaps have opposite signs in the two-gap superconductor the steps with odd index are enhanced, whereas in the s-wave case the ones with even index have larger values. The existence of the fractional Shapiro steps is also predicted.