Majorana edge and end states in planar Josephson junctions

TL;DR

This paper theoretically explores the localization and transition of Majorana states in planar Josephson junctions, revealing how magnetic fields and phase differences influence their edge or end localization, with implications for topological quantum computing.

Contribution

It introduces the concept of transition between end-like and edge-like Majorana states in planar JJs and analyzes their behavior under various tuning parameters and disorder effects.

Findings

Majorana states can be localized at ends or edges depending on parameters.

Transitions between end-like and edge-like states can be controlled by magnetic field and phase difference.

Edge-like Majorana states can serve as interconnects between topological junctions.

Abstract

We theoretically investigate the localization properties of Majorana states (MSs) in proximitized, planar Josephson Junctions (JJs) oriented along different crystallographic orientations and in the presence of an in-plane magnetic field and Rashba and Dresselhaus spin-orbit couplings. We show that two types of MSs may emerge when the junction transits into the topological superconducting state. In one case, referred to as end-like MSs, the Majorana quasiparticles are mainly localized inside the normal region at the opposite ends of the junction. In contrast, edge-like MSs extend along the opposite edges of the system, perpendicular to the junction channel. We show how the MSs can transit from end-like to edge-like and vice versa by tuning the magnetic field strength and/or the superconducting phase difference across the junction. In the case of phase-unbiased JJs the transition may occur as the ground state phase difference self-adjusts its value when the Zeeman field is varied. We propose exploiting the extended nature of edge-like MSs as effective interconnects enabling the coupling between topological states in adjacent planar JJs. The impact of electrostatic disorder on the MSs is also analyzed.