Nanowires with strong Rashba spin-orbit coupling, such as indium arsenide or indium antimonide nanowires, have been investigated in recent years as potential host systems for topological superconductivity and Majorana bound states. In our work, we have studied theoretically the ramifications of the interplay between electron-electron interactions and Rashba spin-orbit coupling in such nanowires. One of the main experimental probes of Rashba spin-orbit coupling in nanowires is a partially gapped electron spectrum due to the application of a magnetic field perpendicular to the Rashba axis. We have shown that in a quasi-one-dimensional wire, the interplay between interactions and Rashba spin-orbit coupling can open a very similar partial gap even in the absence of magnetic field. These two types of gap, caused by magnetic fields or interactions respectively, can be distinguished in experiments by probing response functions. We argue that analogous effects occur in the edge states of two-dimensional topological insulators. This interaction-induced gap changes the topological properties of the wire profoundly: when coupled to a superconductor via the proximity effect such a nanowire can host exotic topological bound states known as Z4-parafermions. The latter are generalizations of Majorana bound states and have great potential in topological quantum computation. In nanowires, they can be experimentally identified by their signatures in spin-dependent response functions and a characteristic topological Josephson effect. Our results thus provide an experimentally feasible avenue to engineer parafermionic bound states.

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Thomas Schmidt, "Correlated electrons in nanowires with Rashba spin-orbit coupling (Conference Presentation)," Proc. SPIE 11090, Spintronics XII, 110903X (Presented at SPIE Nanoscience + Engineering: August 15, 2019; Published: 10 September 2019); https://doi.org/10.1117/12.2528425.6083794192001.