Topological superconductivity by engineering noncollinear magnetism in magnet/superconductor heterostructures: A realistic prescription for the two-dimensional Kitaev model

We report on a realistic and rather general scheme where noncollinear magnetic textures proximitized with the most common $s$-wave superconductor can appear as the alternative to $p$-wave superconductor---the prime proposal to realize two-dimensional (2D) Kitaev model for topological superconductors (TSCs) hosting Majorana flat edge mode (MFEM). A general minimal Hamiltonian suitable for magnet/superconductor heterostructures reveals robust MFEM within the gap of Shiba bands due to the emergence of an effective ``${p}_{x}+{p}_{y}$''-type $p$-wave pairing, spatially localized at the edges of a 2D magnetic domain of spin spiral. We finally verify this concept by considering Mn (Cr) monolayer grown on an $s$-wave superconducting substrate Nb(110) under strain [Nb(001)]. In both 2D cases, the antiferromagnetic spin-spiral solutions exhibit robust MFEM at certain domain edges that is beyond the scope of the trivial extension of one-dimensional (1D) spin-chain model in 2D. This approach, particularly when the MFEM appears in the TSC phase for such heterostructure materials, offers a perspective to extend the realm of the TSC in 2D.