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-deGennes) 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 nontrivial 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.

中文翻译：

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二维手性波约瑟夫森结中马约拉纳束缚态的特征和奇偶效应

我们描述了由耦合介观手性形成的约瑟夫森结的拓扑特征$p$波超导岛。通过对低洼 BdG (Bogoliubov-deGennes) 光谱的分析和数值研究，我们通过应用垂直磁场确定了约瑟夫森涡旋中成核的局部 MBS（Majorana 束缚态）。此外，我们证明存在一个扩展的 MBS，该 MBS 在耦合岛的外围周围离域，这对约瑟夫森超电流和结的相位动力学具有可测量的影响。特别是，我们预测了临界电流衍射图案的变化，其中奇数整数通量节点以费米子奇偶性相关的方式被提升。我们在 RCSJ 框架内模拟了热噪声和宏观量子隧穿的竞争随机效应，并展示了双峰临界电流分布的出现。我们证明了增加奇偶性转变率抑制了分布的双峰性质，因此强烈强调了多体基态的非平凡奇偶性依赖性质。最后，我们考虑了具有三个岛的三角连接几何，并讨论了通过移动它们所绑定的约瑟夫森涡旋来编织马约拉纳绑定状态的可能方案。