Quantum Phase Transitions in Proximitized Josephson Junctions

TL;DR

This paper provides a detailed microscopic analysis of quantum phase transitions in Josephson junctions, revealing they originate from proximity-induced magnetic defects and are not necessarily linked to Majorana zero modes.

Contribution

It offers a fully consistent solution to the Bogoliubov-de Gennes equations for complex junctions, clarifying the origin of QPTs and challenging assumptions about their relation to Majorana physics.

Findings

QPTs originate from proximity-induced magnetic defects.

Standard self-energy approximations may be insufficient.

QPTs do not require spin-orbit coupling or Majorana modes.

Abstract

We study fermion-parity-changing quantum phase transitions (QPTs) in platform Josephson junctions. These QPTs, associated with zero-energy bound states, are rather widely observed experimentally. They emerge from numerical calculations frequently without detailed microscopic insight. Importantly, they may incorrectly lend support to claims for the observations of Majorana zero modes. In this paper we present a fully consistent solution of the Bogoliubov-de Gennes equations for a multi-component Josephson junction. This provides insights into the origin of the QPTs. It also makes it possible to assess the standard self energy approximations which are widely used to understand proximity coupling in topological systems. The junctions we consider are complex and chosen to mirror experiments. Our full proximity calculations associate the mechanism behind the QPT as deriving from a spatially extended, proximity-induced magnetic "defect". This defect arises because of the insulating region which effects a local reorganization of the bulk magnetization in the proximitized superconductor. Our results suggest more generally that QPTs in Josephson junctions generally do not require the existence of spin-orbit coupling and should not be confused with, nor are they indicators of, Majorana physics.