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

Automated summary

We have constructed a three-dimensional second-order topological insulator using weakly tunnel-coupled Rashba nanowires, which exhibits gapless helical hinge states. By choosing suitable interwire tunnelings, we have demonstrated that the system has fully gapped bulk and surfaces, while hosting gapless helical hinge states along a path of hinges determined by the interwire tunnelings hierarchy and boundary termination. Moreover, our coupled-wires approach allows for the incorporation of electron-electron interactions, and at specific filling factors, we have shown that strong enough electron-electron interactions can drive the system into a fractional second-order topological insulator phase with hinge states carrying only a fraction e/p of the electronic charge e for an odd integer p.