Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires

We construct a model of a three-dimensional chiral second-order topological insulator (SOTI) from an array of weakly coupled nanowires. We show that, in a suitable parameter regime, the interplay between rotating magnetic fields and spatially modulated interwire tunnelings leads to the opening of gaps in the bulk and surface spectrum of the system, while one or more chiral hinge states propagating along a closed path of one-dimensional hinges are left gapless. The exact path of these hinge states is determined by the hierarchy of interwire couplings and the boundary termination of the sample. Depending on the ratio between the period of the rotating magnetic field and the Fermi wavelength, our model can realize both integer and fractional chiral SOTIs. The fractional regime emerges in the presence of strong electron-electron interactions and features hinge states carrying only a fraction $e/p$ of the electronic charge $e$ for a positive odd integer $p$.