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

TL;DR

This paper explores quantum phase transitions in a topological Josephson junction with a ferromagnetic layer, predicting Berezinskii-Kosterlitz-Thouless transitions and complex phase diagrams involving Majorana fermions and magnetic anisotropies.

Contribution

It introduces the prediction of BKT transitions in a topological superconductor-ferromagnet-superconductor junction using mean-field and renormalization group analysis, including emergent effective easy-plane scenarios.

Findings

Prediction of BKT transitions in the system

Identification of emergent easy-plane due to anisotropy

Conjecture of a comprehensive phase diagram with multicritical points

Abstract

We investigate quantum phase transitions in a topological Josephson junction with an embedded ferromagnetic layer, revealing a rich landscape of critical phenomena. The low-energy excitations comprise Majorana fermions propagating along the junction, coupled to the magnons in the ferromagnet. Based on mean-field and renormalization group arguments, we predict Berezinskii-Kosterlitz-Thouless (BKT) transitions in this system, both in the case of a magnetic easy-plane and weak easy-axis anisotropy. In the latter case, this is based on an emergent 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. It covers BKT transitions as well as exotic multicritical and supersymmetric points known from related models of interacting real fermions and bosons.