Josephson junction detectors for Majorana modes and Dirac fermions

TL;DR

This paper proposes a phase-sensitive method using Josephson junction I-V characteristics to detect Majorana modes and Dirac fermions, revealing unique subharmonic steps and oscillatory behaviors.

Contribution

It introduces a novel detection technique based on subharmonic Shapiro steps and devil staircase features in Josephson junctions hosting Majorana and Dirac quasiparticles.

Findings

Majorana hosting junctions show subharmonic odd Shapiro steps without 2π periodicity.

Distinct devil staircase structures differentiate Majorana junctions from conventional ones.

Dirac quasiparticle junctions exhibit oscillatory Shapiro step widths linked to transmission resonances.

Abstract

We demonstrate that the current-voltage (I-V) characteristics of resistively and capacitively shunted Josephson junctions (RCSJs) hosting localized subgap Majorana states provides a phase sensitive method for their detection. The I-V characteristics of such RCSJs, in contrast to their resistively shunted counterparts, exhibit subharmonic odd Shapiro steps; such steps occur even in the absence of any $2\pi$ periodic terms in the current-phase relation of these junctions. These steps, owing to their subharmonic nature, exhibit qualitatively different properties compared to harmonic odd steps of conventional junctions. In addition, the RCSJs hosting Majorana bound states also display an additional sequence of steps in the devil staircase structure seen in their I-V characteristics; such sequence of steps make their I-V characteristics qualitatively distinct from that of their conventional counterparts. A similar study for RCSJs with graphene superconducting junctions hosting Dirac-like quasiparticles reveals that the Shapiro step width in their I-V curves bears a signature of the transmission resonance phenomenon of their underlying Dirac quasiparticles; consequently, these step widths exhibit a $\pi$ periodic oscillatory behavior with variation of the junction barrier potential. We discuss experiments which can test our theory.