Multi-locational Majorana Zero Modes

Beyond the framework of the bulk-boundary correspondence, we predict the emergence of a Majorana zero mode that is not bounded at one end of a topological superconductor as conventional, but splits into multiple parts which are located at the distant ends of different topological superconductors. We refer to this remarkable zero mode, which exhibits simultaneously the Majorana property and extreme nonlocality, as a multi-locational Majorana zero mode. Specifically, we discuss multi-locational Majorana zero modes in a three-terminal Josephson junction consisting of topological superconductors, which forms an elemental qubit of fault-tolerant topological quantum computers. The multi-locational Majorana zero modes give rise to highly entangled and anomalously long-ranged nonlocal resonant transport phenomena, which can be utilized to verify conclusively the realization of a fully functional topological three-terminal Josephson junction.