Fractional second-order topological insulator from a three-dimensional coupled-wires construction

We construct a three-dimensional second-order topological insulator with gapless helical hinge states from an array of weakly tunnel-coupled Rashba nanowires. For suitably chosen interwire tunnelings, we demonstrate that the system has fully gapped bulk as well surfaces, but hosts Kramers pair propagating along path hinges is determined by hierarchy tunnelings and boundary termination system. Furthermore, coupled-wires approach allows us to incorporate electron-electron interactions into our description. At suitable filling factors individual wires, show sufficiently strong can drive fractional phase carrying only fraction $e/p$ electronic charge $e$ for odd integer $p$.