Majorana fermions in spin-orbit-coupled ferromagnetic Josephson junctions

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 nontrivial topological phase and a superconducting phase difference φ=π 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 φ.