Majorana bound states in hybrid two-dimensional Josephson junctions with ferromagnetic insulators

P Virtanen,E Strambini,A Braggio,F S Bergeret,F Giazotto

doi:10.1103/physrevb.98.020501

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.

Highlights

Rapid CommunicationsBy starting from a generic Josephson hybrid planar setup, we present an exhaustive analysis of the interplay between the superconducting and magnetic proximity effects and the conditions under which the structure undergoes transitions to a nontrivial topological phase
Majorana bound states (MBS) [1] have been proposed as a building block for solid-state topological quantum computation [2]
Different setups have been discussed theoretically [3,4,5,6,7,8,9,10], many of them relying on the combination of materials with strong spin-orbit coupling, superconductors, and external magnetic field

Summary

Rapid Communications

By starting from a generic Josephson hybrid planar setup, we present an exhaustive analysis of the interplay between the superconducting and magnetic proximity effects and the conditions under which the structure undergoes transitions to a nontrivial topological phase. We address the 2D bound-state problem by using a general transfer-matrix approach that reduces the problem to an effective 1D Hamiltonian. This allows for a straightforward study of the 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. We show the energy spectrum, the free energy, and the multiterminal Josephson current of the setup

Introduction

We define the projectors

Conclusions