Magnetic flux induced higher-order topological superconductivity

Higher-order topological superconductivity typically depends on spin-orbit interaction, and often necessitates well-designed sample structures, nodal superconducting pairings, or complex magnetic order. In this work, we propose a model that incorporates a Zeeman field, antiferromagnetic order, and $s$-wave superconducting pairing, all without the need for spin-orbit interaction. In a two-dimensional system, we realize a second-order topological superconductor by utilizing a staggered flux, provided that the Zeeman field is oriented perpendicular to the magnetic order moments. In three-dimensional systems, we achieve second- and third-order topological superconductors in theory, through stacking the two-dimensional second-order topological superconductor.