  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.
