Josephson junction detectors for Majorana modes and Dirac fermions

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.

v3: 8 pages 5 figs; more comments and numerical estimates; final version accepted fpr publication in PRB

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Cited by in corpus (8)

• Signatures of a 4$\pi$-periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions
• Josephson junctions of multiple superconducting wires
• Detecting topological superconductivity using low-frequency doubled Shapiro steps
• Josephson junctions of Weyl and multi-Weyl semimetals
• Devil's Staircases in SFS Josephson Junctions
• Magnetization induced dynamics of a Josephson junction coupled to a nanomagnet
• Complexity of Shapiro steps
• Embedded Majorana Islands