Majorana fermions in spin-orbit coupled ferromagnetic Josephson junctions

TL;DR

This paper investigates the emergence and detection of Majorana fermions in two-dimensional spin-orbit coupled ferromagnetic Josephson junctions, revealing conditions for their localization and properties based on topological phases and phase differences.

Contribution

It identifies specific conditions under which Majorana modes appear in 2D ferromagnetic SNS junctions, including delocalized and localized types, and proposes experimental detection methods.

Findings

Delocalized Majorana fermions appear at phase difference π in the N region.

Localized Majorana fermions occur at SN interfaces when S and N are in different topological phases.

Majorana modes depend on the topological phase and Fermi surface separation.

Abstract

We study all possible Majorana modes in two-dimensional spin-orbit coupled ferromagnetic superconductor-normal state-superconductor (SNS) Josephson junctions and propose experiments to detect them. With the S region in a non-trivial topological phase and a superconducting phase difference $\phi = \pi$ across the junction, two delocalized Majorana fermions with no excitation gap appear in the N region. In addition, if S and N belong to different topological phases and have well-separated the Fermi surfaces, localized Majorana fermions with a finite excitation gap also emerge at both SN interfaces for all $\phi$.