Topological Superconductivity hosting Majorana States in Magnet/Superconductor Heterostructures

Abstract

Our theoretical investigation explores a feasible route to engineer the two-dimensional (2D) Kitaev model of first-order topological superconductivity (TSC) introducing a magnetic spin texture. The main outcome of 2D Kitaev’s model is that a px + py type superconductor can exhibit a gapless topological superconducting phase in bulk hosting non-dispersive Majorana flat edge mode (MFEM) at the boundary. Our proposed general minimal model Hamiltonian is suitable to describe magnet/superconductor heterostructures. It reveals robust MFEM within the emergent gap of Shiba bands, spatially localised at the edges of a 2D magnetic domain of spin- spiral. We finally verify this concept from real material perspectives by considering Mn (Cr) monolayer grown on an s-wave superconducting substrate, Nb(110) under strain (Nb(001)). In both the 2D cases, the antiferromagnetic spin-spiral solutions exhibit robust MFEM at certain domain edges. This approach, particularly when the MFEM appears in the TSC phase for such heterostructure materials, offers significant prospect to extend the realm of TSC in 2D. Very recently, we expand this theoretical framework for engineering a 2D second-order topological superconductor (SOTSC) by utilizing a heterostructure: incorporating noncollinear magnetic textures between an s-wave superconductor and a 2D quantum spin Hall insulator. It stabilizes the SOTSC phase within the Shiba band, resulting in Majorana corner modes (MCMs) at the four corners of a 2D domain. The calculated non-zero quadrupole moment characterizes the bulk higher-order topology. Analytically calculated effective pairings in the bulk illuminate the microscopic behaviour of the SOTSC. Such first and second order Majorana modes are believed to be the building blocks for the fault-tolerant topological quantum computation.

Reference: Phys. Rev. B (Letter) 109, L041409 (2024) .
Phys. Rev. B (Letter) 109, L121301 (2024).