标题： 迈向可扩展编织：平面约瑟夫森结中几乎任意磁场方向下的拓扑超导性 显示英文标题

标题： Towards Scalable Braiding: Topological Superconductivity Unlocked under Nearly Arbitrary Magnetic Field Directions in Planar Josephson Junctions

摘要： 马约拉纳零能模（MZM），以其非局域性和非阿贝尔统计特性而著称，是容错拓扑量子计算研究的核心。平面约瑟夫森结（PJJ）作为一种有前景的平台，展现了稳健且可调谐的MZM。然而，人们对拓扑超导性对外加磁场方向的敏感性担忧，成为可扩展网络架构的主要障碍。 我们发现，平面约瑟夫森结中的拓扑超导性在几乎任意面内磁场方向下本质上仍然存在。在磁场方向不匹配时，整体能隙看似坍塌，这并非源于超导性的破坏，而是由于来自其他动量点的新兴平移体态掩盖了能隙和MZM。 通过沿结引入空间调制以散射和平移这些体态，我们恢复了全局拓扑能隙并重新显现了MZM。令人惊讶的是，这种空间调制的平面约瑟夫森结使拓扑超导性对非对齐磁场具有鲁棒性，从而实现了复杂结网络中MZM的存活，并促进了它们的编织操作。 我们提出了一种可扩展的MZM编织与融合协议，通过相位或门控制，开辟了拓扑量子计算新路径。 显示英文摘要

摘要： Majorana zero modes (MZM), distinguished by their non-locality and non-Abelian statistics, are central to the pursuit of fault-tolerant topological quantum computing. Planar Josephson junctions (PJJ) have emerged as a promising platform, offering robust and tunable MZM. However, the perceived sensitivity of topological superconductivity to the magnetic field orientation has posed a major obstacle, particularly for scalable network architectures. Here, we uncover that topological superconductivity in PJJ fundamentally persists under nearly arbitrary in-plane magnetic field directions. The apparent collapse of the global gap under misaligned fields originates not from the destruction of superconductivity itself, but from emergent shifted bulk states from other momentum points, which obscure the gap and MZM. By introducing spatial modulations along the junction to scatter and gap out these bulk states, we restore the global topological gap and recover visible MZM. Remarkably, the spatially modulated PJJs render topological superconductivity robust against maligned fields, thereby enabling MZM survival across complex junction networks and facilitating their braiding. We propose a scalable protocol for MZM braiding and fusion with phase or gate control, opening new routes toward scalable topological quantum computing.