Topological Superconductivity and Majorana Fermions in RKKY Systems

We consider quasi one-dimensional RKKY systems in proximity to an s-wave superconductor [1]. 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 $1/2k_F$ [2,3] . 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 [3-6]. [1] J. Klinovaja, P. Stano, A. Yazdani, and D. Loss, Phys. Rev. Lett. 111, 186805 (2013). [2] B. Braunecker, G. I. Japaridze, J. Klinovaja, and D. Loss, Phys. Rev. B 82, 045127 (2010). [3] J. Klinovaja, P. Stano, and D. Loss, Phys. Rev. Lett. 109, 236801 (2012). [4] J. Klinovaja and D. Loss, Phys. Rev. B 86, 085408 (2012). [5] J. Klinovaja and D. Loss, Phys. Rev. X 3, 011008 (2013). [6] J. Klinovaja and D. Loss, Phys. Rev. B 88, 075404 (2013).