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

Pankaj Sharma, Narayan Mohanta

TL;DR

The paper addresses realizing and stabilizing Majorana bound states in planar Josephson junctions, a two-dimensional platform with tunable chemical potential, magnetic field, and phase difference. The authors analyze a symmetric planar JJ under an in-plane magnetic field, identify three topological regimes with distinct MBS localization, including MBS at the ends of the middle channel and at the ends of the superconducting leads. Disorder robustness is demonstrated: non-magnetic fluctuations in chemical potential do not destroy MBS, and the two-dimensional geometry reduces sensitivity, with moderate disorder potentially reducing MBS splitting by minimizing wavefunction overlap. Lead width controls localization patterns and phase diagrams in the magnetic field and phase difference plane, highlighting experimental routes to observe multiple MBS in planar JJs.

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.

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

TL;DR

The paper addresses realizing and stabilizing Majorana bound states in planar Josephson junctions, a two-dimensional platform with tunable chemical potential, magnetic field, and phase difference. The authors analyze a symmetric planar JJ under an in-plane magnetic field, identify three topological regimes with distinct MBS localization, including MBS at the ends of the middle channel and at the ends of the superconducting leads. Disorder robustness is demonstrated: non-magnetic fluctuations in chemical potential do not destroy MBS, and the two-dimensional geometry reduces sensitivity, with moderate disorder potentially reducing MBS splitting by minimizing wavefunction overlap. Lead width controls localization patterns and phase diagrams in the magnetic field and phase difference plane, highlighting experimental routes to observe multiple MBS in planar JJs.

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.
Paper Structure (1 section, 2 figures)

This paper contains 1 section, 2 figures.

Table of Contents

  1. Introduction

Figures (2)

  • Figure 1: (a) Schematic of a planar Josephson junction, showing two superconducting regions (in blue) deposited on a semiconductor interface (in grey) which forms a two-dimensional electron gas. A magnetic field ${\bf B}$ is applied parallel to the junction length in the entire system to tune it to the topological superconducting phase. (b) Localization of MBS in the three topological superconducting regimes.
  • Figure :