Spin-Dependent Signatures of Majorana Vortex Fusion within Planar Josephson Junctions

TL;DR

This paper explores how Majorana vortices fuse in planar Josephson junctions with spin-orbit coupling, revealing magnetic and tunnelling signatures that could aid in topological quantum computing.

Contribution

It introduces a new method to detect Majorana fusion outcomes via spin-resolved conductance and provides a detailed microscopic model of the process.

Findings

Fusion induces a parity-dependent magnetic moment.

Spin-resolved conductance reveals Majorana fusion signatures.

Effective Hamiltonian describes observed phenomena.

Abstract

We investigate the magnetic characteristics and tunnelling signatures of a planar Josephson junction with Rashba spin-orbit coupling during the fusion of two Majorana vortices. By employing the topological phase diagram and conducting tight-binding simulations of the proposed device, we demonstrate that this fusion process induces a parity-dependent magnetic moment aligned with the junction axis. We further propose a method to probe the spin properties of the fusing Majorana zero modes through spin-resolved Andreev conductance measurements at the junction endpoints. To support our findings, we derive a low-energy effective Hamiltonian that provides a detailed microscopic description of the numerically observed phenomena. Our analysis enables the detection of Majorana fusion outcome from accessible spin current measurements, thus paving the way for future experimental verification and potential applications in topological quantum computation.