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arXiv · 1905.00885

Fractional Topological Superconductivity and Parafermion Corner States

Katharina Laubscher·Daniel Loss·Jelena Klinovaja
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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.

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Katharina Laubscher, Daniel Loss, Jelena Klinovaja. 2019-05-02. Fractional Topological Superconductivity and Parafermion Corner States. https://doi.org/10.1103/physrevresearch.1.032017

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