Self-organized topological state in the magnetic chain on the surface of a superconductor

TL;DR

This paper investigates how a chain of magnetic atoms on a superconductor surface naturally adjusts its magnetic structure to maintain a topological phase supporting Majorana fermions, even in realistic 2D models with imperfections.

Contribution

It demonstrates that the self-organization property of the magnetic chain persists in a realistic 2D model with self-consistent treatment, despite a reduced topological phase region.

Findings

Self-organization of magnetic moments persists in 2D models.

Topological phase remains robust against moderate disorder.

The phase diagram for the 2D model is slightly smaller than the 1D case.

Abstract

Electronic states associated with a chain of magnetic adatoms on the surface of an ordinary s- wave superconductor have been shown theoretically to form a one dimensional topological phase with unpaired Majorana fermions bound to its ends. In a simple 1D effective model the system exhibits an interesting self-organization property: the pitch of the spiral formed by the adatom magnetic moments tends to adjust itself so that electronically the chain remains in the topological phase whenever such a state is physically accessible. Here we examine the physics underlying this self-organization property in the framework of a more realistic 2D model of a superconducting surface coupled to a 1D chain of magnetic adatoms. Treating both the superconducting order and the magnetic moments selfconsistently we find that the system retains its self-organization property, even if the topological phase extends over a somewhat smaller portion of the phase diagram compared to the 1D model. We also study the effect of imperfections and find that, once established, the topological phase survives moderate levels of disorder.