Fate and remnants of Majorana zero modes in a quantum wire array

Experimental signatures of Majorana zero modes in a single superconducting quantum wire with spin-orbit coupling have been reported as zero-bias peaks in tunneling spectroscopy. We study whether these zero modes can persist in an array of coupled wires, and if not, what their remnant might be. The bulk exhibits topologically distinct gapped phases and an intervening gapless phase. Even though the bulk pairing structure is topological, the interaction between Majorana zero modes and superfluid phases leads to spontaneous time-reversal symmetry breaking. Consequently, edge supercurrent loops emerge and edge Majorana fermions are in general gapped out except when the number of chains is odd, in which case one Majorana fermion survives.