Topological Superconductivity and Majorana Fermions in RKKY Systems

Abstract

We consider quasi-one-dimensional Ruderman-Kittel-Kasuya-Yosida (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 wave vector. The magnetic helix is equivalent to a uniform magnetic field and very strong spin-orbit interaction (SOI) with an effective SOI length 1/2k(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.

Spin and charge signatures of topological superconductivity in Rashba nanowires

“…One of the hallmarks of such phases, in particular of topological superconductivity, are zero-energy modes such as Majorana fermions (MF) that emerge at the edges of the system. Various candidate materials can host such topological states [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] but one of the most promising platforms are semiconducting nanowires of InAs or InSb material, with strong Rashba spin orbit interaction (SOI), subjected to an external magnetic field and in proximity to an s-wave superconductor [22,23]. Experimental evidence has been reported for topological phases in such wires [24][25][26][27][28][29][30][31] as well as in magnetic atomic chains on superconducting substrates [32][33][34].…”

DIII topological superconductivity with emergent time-reversal symmetry

“…Topological superconductors have been intensively pursued in recent years [1][2][3] because the Majorana fermions which are localized to their boundaries have potential applications in the development of a topological quantum computer [4,5]. The most promising proposals to date for engineering topological superconductivity involve coupling a conventional superconductor either to a nanowire with Rashba spin-orbit interaction that is subjected to an external magnetic field or to a ferromagnetic atomic chain [27][28][29][30][31][32][33][34].Additionally, there have been several proposals to engineer topological superconductors in symmetry class DIII. Such systems possess both particle-hole symmetry and time-reversal symmetry [35], with the presence of time-reversal symmetry ensuring that the Majorana fermions existing at the boundaries of class DIII topological superconductors come in Kramers pairs.…”

Majorana Fermions and Topology in Superconductors

“…[102][103][104][105][106][107][108] A simple example is a 1D s-wave superconductor coupled with helical magnetic order of localized spins via the exchange interaction…”

“…103,[105][106][107] Here k F is the Fermi wave number of the 1D itinerant electron system, and S is the magnitude of the localized spin. Then, the unitary transformation,…”