Characterization of Shapiro steps in the presence of a 4{\pi}-periodic Josephson current

TL;DR

This paper investigates how Shapiro steps in Josephson junctions are affected by a 4π-periodic current component, providing insights into identifying Majorana modes through characteristic step suppression.

Contribution

It analyzes the response of Shapiro steps to a 4π-periodic Josephson current, identifying parameter conditions for their full suppression and implications for Majorana mode detection.

Findings

Full suppression of the first lobe indicates 4π-periodic current presence.

Specific parameter ranges of frequency and McCumber parameter enable step suppression.

Large I_c R_N product and junction capacitance are needed for observing period doubling.

Abstract

The Majorana zero-energy modes (MZMs) residing at the boundary of topological superconductors have attracted a great deal of interest recently, as they provide a platform to explore fundamental physics such as non-Abelian statistics, as well as fault-tolerant quantum computation. Period doubling of Shapiro steps in a Josephson junction under microwave irradiation has been regarded as strong evidence for the emergence of the MZMs at the junction edges. However, questions remain as to how the Shapiro steps respond to the presence of a 4{\pi}-periodic Josephson current. In this study, we investigated the characteristic features of Shapiro steps with respect to the ratio ({\alpha}) of the 4{\pi}-periodic current to the topologically trivial 2{\pi}-periodic one, as well as the reduced microwave frequency ({\Omega}) and McCumber parameter ({\beta}) of the junction. Our analysis reproduced Shapiro steps similar to those observed experimentally for specific parameter sets of {\alpha},{\Omega} ({\lesssim 0.1}), and {\beta} ({gtrsim 1.0}). Full suppression of the first lobe of the n=1 step guarantees the presence of a 4{\pi}-periodic Josephson current.In addition, we discuss the range of {\Omega} and {\beta} needed for full suppression of the first lobe of the {n=1} step, even for small {\alpha} ({<0.1}). To observe "period-doubled Shapiro steps", even with a small {\alpha}, the junction should have a large {I_c}{R_N} product and sufficiently large junction capacitance.