Abstract
We consider a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires are arranged into two tunnel-coupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is $\pi$. We show that in such a system strong electron-electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of $\mathbb{Z}_{2m}$ parafermion edge modes, where $m$ is an odd integer determined by the position of the chemical potential. Furthermore, upon turning on a weak in-plane magnetic field, the system is driven into a second-order topological superconducting phase hosting zero-energy $\mathbb{Z}_{2m}$ parafermion bound states localized at two opposite corners of a rectangular sample. As a special case, zero-energy Majorana corner states emerge in the non-interacting limit $m=1$, where the chemical potential is tuned to the SOI energy of the single nanowires.
Highlights
The search for topological phases of matter has generated an enormous amount of research
Assuming that the interwire terms are relevant [70] and repeating the analysis of the integer case for the modes given in Eq (10), we find that the bulk of the system is fully gapped, while there is a Kramers pair of gapless modes propagating along the edges of a finite sample
We have studied a system consisting of two layers of coupled Rashba nanowires in the presence of interlayer tunneling and proximity-induced superconductivity of a phase difference of π between the layers
Summary
We consider a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires are arranged into two tunnel-coupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is π. We show that in such a system strong electron-electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of Z2m parafermion edge modes, where m is an odd integer determined by the position of the chemical potential. Upon turning on a weak in-plane magnetic field, the system is driven into a second-order topological superconducting phase hosting zero-energy Z2m parafermion bound states localized at two opposite corners of a rectangular sample. Zero-energy Majorana corner states emerge in the noninteracting limit m = 1, where the chemical potential is tuned to the SOI energy of the single nanowires
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