Signatures of Majorana bound states and parity effects in two-dimensional chiral p-wave Josephson junctions

TL;DR

This paper investigates topological features and Majorana bound states in two-dimensional chiral p-wave Josephson junctions, revealing parity-dependent effects on supercurrent and proposing braiding schemes for Majorana states.

Contribution

It provides a detailed analysis of Majorana bound states in 2D chiral p-wave Josephson junctions, including their localization, impact on supercurrent, and potential for braiding.

Findings

Localized Majorana bound states nucleate in Josephson vortices.

Extended Majorana states influence Josephson supercurrent and phase dynamics.

Parity transitions affect the critical current diffraction pattern and distribution.

Abstract

We characterize topological features of Josephson junctions formed by coupled mesoscopic chiral $p$-wave superconducting islands. Through analytic and numerical studies of the low-lying BdG (Bogoliubov-de Gennes) spectrum, we identify localized MBS (Majorana bound states) nucleated in Josephson vortices by the application of a perpendicular magnetic field. Additionally, we demonstrate the existence of an extended MBS that is delocalized around the outer perimeter of the coupled islands, which has measurable consequences on the Josephson supercurrent and phase dynamics of the junction. In particular, we predict a change in the critical current diffraction pattern in which the odd integer-flux nodes are lifted in a fermion parity-dependent fashion. We model the competing stochastic effects of thermal noise and macroscopic quantum tunneling within the RCSJ framework and show the emergence of a bimodal critical current distribution. We demonstrate that increasing the parity transition rate suppresses the bimodal nature of the distribution, thus strongly emphasizing the non-trivial parity dependent nature of the many-body ground state. Finally, we consider a trijunction geometry with three islands and discuss possible schemes to braid Majorana bound states by moving the Josephson vortices to which they are bound.