Berezinskii–Kosterlitz–Thouless transitions in a topological superconductor–ferromagnet–superconductor junction

We study quantum phase transitions in a long and narrow topological Josephson junction. The low-energy excitations comprise Majorana fermions propagating along the junction, coupled to magnons in an embedded ferromagnetic layer. Based on mean-field and renormalization group arguments, we predict the existence of Berezinskii-Kosterlitz-Thouless transitions in this system, both in the case of a magnetic easy-plane and easy-axis anisotropy. In the easy-axis regime, this is based on an emerging effective easy-plane, spanned by the easy-axis and the component of the magnetization which couples to the Majoranas. We conclude by presenting a conjecture for the full phase diagram of the model.