Model for missing Shapiro steps due to bias-dependent resistance

TL;DR

This paper introduces a phenomenological model explaining the suppression of odd Shapiro steps in Josephson junctions, which can occur even without Majorana modes, challenging their use as exclusive signatures.

Contribution

The model demonstrates how bias-dependent resistance peaks can suppress Shapiro steps, offering an alternative explanation for missing steps in experiments.

Findings

Suppression of odd Shapiro steps can occur without Majorana modes.

Bias-dependent resistance peaks influence Shapiro step visibility.

The model reproduces experimental observations of missing steps.

Abstract

Majorana zero modes are predicted in several solid state systems such as hybrid superconductor-semiconductor structures and topological insulators coupled to superconductors. One of the expected signatures of Majorana modes is the fractional 4$\pi$ Josephson effect. Evidence in favor of this effect often comes from a.c. Josephson effect measurements and focuses on the observation of missing first or higher odd-numbered Shapiro steps. However, the disappearance of the odd Shapiro steps has also been reported in conventional Josephson junctions where no Majorana modes are expected. In this paper, we present a phenomenological model that displays suppression of the odd Shapiro steps. We perform resistively-shunted junction model calculations and introduce peaks in differential resistance as function of the bias current. In the presence of only the standard 2$\pi$ Josephson current, for chosen values of peak positions and amplitudes, we can suppress the odd Shapiro steps, or any steps, thus providing a possible explanation for the observation of missing Shapiro steps.