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

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.