📝 SummarXiv

Abstract

The non-Abelian statistics of Majorana zero modes (MZM) is central to the fault-tolerant topological quantum computing. Planar Josephson junctions (PJJ) are a particularly versatile platform to realize robust topological superconductivity hosting MZM over a large parameter space. However, there is a general understanding that such topological superconductivity is limited to a narrow range of the in-plane magnetic field orientations, providing a major obstacle towards scalable and noncollinear network architectures. Here, we uncover that topological superconductivity in PJJ persists under nearly an arbitrary in-plane magnetic field orientation. The apparent collapse of the global gap under misaligned fields originates not from the destruction of topological superconductivity itself, but from the emergent shifted bulk states from other momenta, which obscure the gap and MZM. With spatial modulations along the junction to scatter and gap out these bulk states, we restore the global topological gap and recover MZM. Remarkably, the spatially modulated PJJ renders topological superconductivity robust against the misaligned fields, thereby enabling MZM survival and facilitating their braiding in complex junction networks. We propose a scalable protocol for MZM braiding and fusion with gate or phase control, opening new routes for scalable topological quantum computing.