Fractional Josephson Vortices and Braiding of Majorana Zero Modes in Planar Superconductor-Semiconductor Heterostructures

TL;DR

This paper explores how magnetic fields and supercurrents influence Majorana zero modes in a 1D topological superconductor within a superconductor-metal-superconductor junction, revealing fractional vortices and a method for braiding Majorana modes.

Contribution

It demonstrates the fractionalization of Josephson vortices into half-vortices and introduces a current-controlled approach for braiding Majorana zero modes in planar heterostructures.

Findings

Josephson vortices can fractionalize into half-vortices.

Majorana zero modes can be braided using supercurrent control.

The system exhibits conditions for stable Majorana modes and vortex fractionalization.

Abstract

We consider the one-dimensional (1D) topological superconductor that may form in a planar superconductor-metal-superconductor Josephson junction in which the metal is is subjected to spin orbit coupling and to an in-plane magnetic field. This 1D topological superconductor has been the subject of recent theoretical and experimental attention. We examine the effect of perpendicular magnetic field and a supercurrent driven across the junction on the position and structure of the Majorana zero modes that are associated with the topological superconductor. In particular, we show that under certain conditions the Josephson vortices fractionalize to half-vortices, each carrying half of the superconducting flux quantum and a single Majorana zero mode. Furthemore, we show that the system allows for a current-controlled braiding of Majorana zero modes.