$\mathbb Z_{2q}$ parafermionic hinge states in a three-dimensional array of coupled nanowires

Abstract: We construct a model of a three-dimensional helical second-order topological superconductor formed by an array of weakly coupled Rashba nanowires. We identify the parameter regime in which there are energy gaps in both the bulk and surface energy spectra, while a pair of gapless helical $\mathbb{Z}_{2q}$ parafermionic modes (with $q$ being an odd integer) remains gapless along a closed path of one-dimensional hinges. The precise trajectory of these hinge modes is dictated by the hierarchy of interwire couplings and the boundary termination of the sample. In the noninteracting limit $q= 1$, the system hosts gapless Majorana hinge modes.