Majorana bound states in hybrid 2D Josephson junctions with ferromagnetic insulators

TL;DR

This paper investigates how hybrid superconductor/ferromagnetic insulator junctions on a 2D electron gas can host Majorana bound states, analyzing topological phase transitions and controllability via superconducting phase tuning.

Contribution

It introduces a transfer matrix approach to analyze topological phases in 2D Josephson junctions with ferromagnetic insulators, enabling control of Majorana states.

Findings

Identification of conditions for topological phase transitions.

Demonstration of spatial control of Majorana states via phase tuning.

Calculation of energy spectrum, free energy, and Josephson current.

Abstract

We consider a Josephson junction consisting of superconductor/ferromagnetic insulator (S/FI) bilayers as electrodes which proximizes a nearby 2D electron gas. By starting from a generic Josephson hybrid planar setup we present an exhaustive analysis of the the interplay between the superconducting and magnetic proximity effects and the conditions under which the structure undergoes transitions to a non-trivial topological phase. We address the 2D bound state problem using a general transfer matrix approach that reduces the problem to an effective 1D Hamiltonian. This allows for straightforward study of topological properties in different symmetry classes. As an example we consider a narrow channel coupled with multiple ferromagnetic superconducting fingers, and discuss how the Majorana bound states can be spatially controlled by tuning the superconducting phases. Following our approach we also show the energy spectrum, the free energy and finally the multiterminal Josephson current of the setup.