Topological Josephson trijunctions as a Majorana source and path

Abstract Majorana bound states (MBSs) are zero-energy localized states in topological superconductors, obeying non-Abelian braiding statistics. Manipulation of mobile MBSs, encompassing their on-demand generation, propagation, and fusion, is essential for braiding MBSs and operating topological qubits. We show that the manipulation is enabled by a trijunction formed on a topological insulator in a perpendicular magnetic field, where three Josephson junctions meet. While the superconducting phases at the trijunction center evolve to cross a boundary between topological and non-topological phase domains, the trijunction offers two distinct dynamics, source/sink and path, depending on the phase boundaries. At a source/sink boundary, two MBSs are pairwise generated at the center, and one of them is ejected to a Josephson junction. The reverse, pair annihilation by collision of two MBSs, can also happen. At a path boundary, an MBS moves from a Josephson junction to the trijunction center or vice versa, without involving other MBSs. Exploiting the two dynamics, fusion and braiding of MBSs can be operated in a trijunction network. We illustrate this with a double trijunction setup, where non-Abelian state evolutions associated with MBSs can be manipulated without dynamical control of the setup and detected by Josephson emission spectroscopy.