Topological Superconductivity and Majorana Fermions in RKKY Systems

TL;DR

This paper demonstrates that quasi-one-dimensional RKKY systems near s-wave superconductors naturally develop a helical magnetic order at 2k_F, leading to topological phases hosting Majorana fermions without chemical potential tuning.

Contribution

It reveals the conditions under which RKKY systems form a topological phase with Majorana fermions via a self-tuned helical magnetic order at 2k_F.

Findings

Helical magnetic order is supported by a 2k_F peak in spin susceptibility.

The magnetic helix mimics a strong spin-orbit interaction.

Systems naturally enter a topological phase with Majorana fermions.

Abstract

We consider quasi one-dimensional RKKY systems in proximity to an s-wave superconductor. We show that a $2k_F$-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 wavevector. The magnetic helix is equivalent to a uniform magnetic field and very strong spin-orbit interaction (SOI) with an effective SOI length $1/2k_F$. 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 $2k_F$ eliminates the need to tune the chemical potential.