Topological Superconductivity and Majorana Fermions in RKKY Systems

TLDR

Quasi‑one‑dimensional RKKY systems coupled to an s‑wave superconductor are studied. The magnetic helix behaves like a uniform magnetic field with very strong spin‑orbit coupling of effective length 1/(2k_F). A 2k_F peak in the superconductor’s spin susceptibility drives helical magnetic order that, in atomic chains or semiconductor nanowires, naturally places the system in a topological phase hosting Majorana fermions without requiring chemical‑potential tuning.

Abstract

We consider quasi-one-dimensional Ruderman-Kittel-Kasuya-Yosida (RKKY) systems in proximity to an $s$-wave superconductor. We show that a $2{k}_{F}$ peak in the spin susceptibility of the superconductor in the one-dimensional limit supports helical order of localized magnetic moments via RKKY interaction, where ${k}_{F}$ is the Fermi wave vector. The magnetic helix is equivalent to a uniform magnetic field and very strong spin-orbit interaction (SOI) with an effective SOI length $1/2{k}_{F}$. We find the conditions to establish such a magnetic state in atomic chains and semiconducting nanowires with magnetic atoms or nuclear spins. Generically, these systems are in a topological phase with Majorana fermions. The inherent self-tuning of the helix to $2{k}_{F}$ eliminates the need to tune the chemical potential.