Multiple Majorana bound states and their resilience against disorder in planar Josephson junctions

TL;DR

This study predicts multiple Majorana bound states in planar Josephson junctions, demonstrating their robustness against disorder and exploring how geometrical parameters influence their topological phases, with implications for experimental realization.

Contribution

It identifies three topological regimes with multiple Majorana states in planar Josephson junctions and analyzes their stability against disorder and geometrical variations.

Findings

Multiple topological regimes with Majorana states identified

Majorana states are robust against non-magnetic disorder

Disorder can reduce Majorana splitting, enhancing stability

Abstract

Planar Josephson junctions are theoretically predicted to harbor zero-energy Majorana bound states (MBS) in a tunable two-dimensional geometry, at the two ends of the middle metallic channel. Here we show that three distinct topological superconducting regimes, governing the localization of the near-zero-energy MBS, appear in these planar Josephson junctions. The topologically-protected MBS appear near the narrow edges of the junction -- not only in the middle metallic channel but also in the superconducting leads which have widths similar to the values used in recent experiments. We incorporate random fluctuation in the chemical potential to investigate the influence of non-magnetic disorder on the localization of the MBS in different topological regimes and find that the MBS are quite robust against disorder because of the two-dimensional geometry. Interestingly, moderate amount of disorder reduces the splitting between the MBS pairs, possibly by minimizing the wave function overlap of the MBS. We also discuss the changes in the topological superconducting phases when the superconducting lead width is varied. Our results reveal a rich structure of the localization of topologically protected multiple MBS in experimentally-accessible planar Josephson junctions, and call for their experimental confirmation.