The demonstration of the non-Abelian properties of Majorana bound states (MBSs) is a crucial step toward topological quantum computing. We theoretically investigate how the fusion of MBSs manifests itself in the current-voltage characteristics of a topological Josephson junction. The junction is assumed to be built on U-shaped quantum spin Hall edges and is supposed to host a Majorana qubit formed by four MBSs. Inter- and intraedge couplings among adjacent MBSs provide two orthogonal components of the rotation axes 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 in the formation of ordinary Shapiro steps is replaced by the intrinsic Rabi oscillations of the Majorana qubit. We coin this phenomenon DC Shapiro steps.

• Received 10 June 2020
• Revised 14 August 2020
• Accepted 15 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.140501