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

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.

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• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Detection of Majorana zero modes bound to Josephson vortices in planar superconductor-topological insulator-superconductor junctions
• Majorana bound state parity exchanges in planar Josephson junctions
• Boundary-induced Majorana coupling in a planar topological Josephson junction
• Designing Phase Sensitive Probes of Monopole Superconducting Order
• Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization
• Unveiling Topological Hinge States in the Higher-Order Topological Insulator WTe${}_2$ Based on the Fractional Josephson Effect
• Theory of reentrant superconductivity in Corbino Josephson junctions
• Emergence of multiple zero modes bound to vortices in extended topological Josephson junctions