Majorana-induced DC Shapiro steps in topological Josephson junctions

TL;DR

This paper theoretically demonstrates that Majorana fusion rules induce unique DC Shapiro steps in topological Josephson junctions, revealing non-Abelian properties through intrinsic Rabi oscillations without external AC drive.

Contribution

It introduces a novel theoretical prediction that Majorana fusion rules cause observable DC Shapiro steps driven by Majorana qubit dynamics in topological Josephson junctions.

Findings

Sequential voltage jumps linked to Majorana Rabi oscillations

Majorana fusion rules influence Josephson effect dynamics

Intrinsic qubit oscillations replace external AC driving in inducing Shapiro steps

Abstract

The demonstration of the non-Abelian properties of Majorana bound states (MBS) is a crucial step toward topological quantum computing. We theoretically investigate how Majorana fusion rules manifest themselves in the current-voltage characteristics of a topological Josephson junction. The junction is built on U-shaped quantum spin Hall edges and hosts a Majorana qubit formed by four MBS. Owing to Majorana fusion rules, inter- and intra-edge couplings among adjacent MBS provide two orthogonal components in the rotation axis of the Majorana qubit. We show that the interplay of the dynamics of the superconductor phase difference and the Majorana qubit governs the Josephson effect. Strikingly, we identify sequential jumps of the voltage across the junction with increasing DC current bias without external AC driving. Its role is replaced by the intrinsic Rabi oscillations of the Majorana qubit. This phenomenon, DC Shapiro steps, is a manifestation of the non-trivial fusion rules of MBS.