Spin-polarized edge currents and Majorana fermions in one- and two-dimensional topological superconductors

TL;DR

This paper explores the properties of topological superconductors with ferromagnetic impurities, revealing spin-polarized edge currents and Majorana fermions, with implications for understanding topological states and zero-dimensional impurity physics.

Contribution

It provides a self-consistent analysis of edge states and Majorana fermions in 1D and 2D topological superconductors with ferromagnetic impurities, highlighting spin polarization effects.

Findings

Edge states produce spin-polarized edge currents.

Persistent currents flow opposite to edge state dispersion.

Majorana fermions are spin-polarized and linked to edge currents.

Abstract

We investigate the persistent currents, spin-polarized local density of states, and spectral functions of topological superconductors constructed by placing ferromagnetic impurities on top of an s-wave superconductor with Rashba spin-orbit interaction. We solve self-consistently for the superconducting order parameter and investigate both two-dimensional blocks and one-dimensional wires of ferromagnetic impurities, with the magnetic moments pointing both perpendicular and parallel to the surface. We find that the topologically protected edge states of ferromagnetic blocks give rise to spin-polarized edge currents, but that the total persistent current flows in opposite direction to what is expected from the dispersion relation of the edge states. We also show that the Majorana fermions at the end points of one-dimensional wires are spin-polarized, which can be directly related to the spin-polarization of the edge currents of two-dimensional blocks. Connections are also made to the physics of the Yu-Shiba-Rusinov states for zero-dimensional impurities.