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Realizing Majorana modes in topological superconductors, i.e., thecondensed-matter counterpart of Majorana fermions in particle physics, may leadto a major advance in the field of topologically-protected quantum computation.Here, we introduce one-dimensional, counterpropagating, and dispersive Majoranamodes as bulk excitations of a periodic chain of partially-overlapping,zero-dimensional Majorana modes in proximitized nanowires viaperiodically-modulated fields. This system realizes centrally-extendedquantum-mechanical supersymmetry with spontaneous partial supersymmetrybreaking. The massless Majorana modes are the Nambu-Goldstone fermions(Goldstinos) associated with the spontaneously broken supersymmetry. Theirexperimental fingerprint is a dip-to-peak transition in the zero-biasconductance, which is generally not expected for Majorana modes overlapping ata finite distance. Moreover, the Majorana modes can slide along the wire byapplying a rotating magnetic field, realizing a "Majorana pump". This maysuggest new braiding protocols and implementations of topological qubits.

1D Majorana Goldstinos and partial supersymmetry breaking in quantum wires