Optimal Conditions for Observing Fractional Josephson Effect in Topological Josephson Junctions

TL;DR

This study identifies optimal experimental conditions, such as junction capacitance and microwave frequency, for observing the fractional Josephson effect in topological Josephson junctions containing Majorana bound states.

Contribution

The paper introduces a modified resistively and capacitively shunted junction model to predict conditions enhancing the fractional Josephson effect in topological JJs.

Findings

Increased junction capacitance enhances odd Shapiro step suppression.

Higher IcRn product improves fractional effect visibility.

Lower microwave frequency favors the observation of 4π-periodic supercurrent.

Abstract

Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$\pi$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evidence of the fractional ac Josephson effect, is enhanced significantly by the increase in the junction capacitance and IcRn product as well as the decrease in the microwave frequency even for the same portion of the 4$\pi$-periodic supercurrent. Our study provides the optimal conditions for observing the fractional ac Josephson effect; furthermore, our new model can be used to precisely quantify the topological supercurrent from the experimental data of topological JJs.