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

TL;DR

This paper presents a construction of a three-dimensional fractional second-order topological insulator with gapless helical hinge states, using coupled Rashba nanowires, and explores the effects of electron-electron interactions.

Contribution

It introduces a coupled-wires approach to realize fractional second-order topological insulators with fractional hinge states, incorporating electron interactions into the model.

Findings

Realization of a fully gapped bulk and surface with gapless hinge states

Demonstration of fractional hinge states carrying fractional charge

Inclusion of electron-electron interactions leading to fractional topological phases

Abstract

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 $p$.