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The emergence of zero energy states in non-topological superconductorsrepresents an inevitable problem that obscures the proper identification ofzero energy Majorana bound states (MBSs) and prevents their use astopologically protected qubits. In this Research Letter we investigate longsuperconductor-normal-superconductor junctions where trivial zero energystates, robust over a large range of parameters, appear as a result of helicityand confinement in the normal region. We demonstrate that both equilibriumsupercurrents and critical currents are sensitive to variations in the lengthof the superconductor regions in the topological phase hosting MBSs, but,remarkably, no such length dependence exists when robust, but trivial, zeroenergy states are present. This strikingly different response originates fromthe non-local nature of the MBSs and we, therefore, propose it as a simpleprotocol for distinguishing between trivial and topological zero energy states.

Distinguishing trivial and topological zero energy states in long nanowire junctions