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We put forth a theoretical framework for engineering a two-dimensional (2D)second-order topological superconductor (SOTSC) by utilizing a heterostructure:incorporating noncollinear magnetic textures between an s-wave superconductorand a 2D quantum spin Hall insulator. It stabilizes the higher ordertopological superconducting phase, resulting in Majorana corner modes (MCMs) atfour corners of a 2D domain. The calculated non-zero quadrupole momentcharacterizes the bulk topology. Subsequently, through a unitarytransformation, an effective low-energy Hamiltonian reveals the effects ofmagnetic textures, resulting in an effective in-plane Zeeman field andspin-orbit coupling. This approach provides a qualitative depiction of thetopological phase, substantiated by numerical validation within exactreal-space model. Analytically calculated effective pairings in the bulkilluminate the microscopic behavior of the SOTSC. The comprehension of MCMemergence is aided by a low-energy edge theory, which is attributed to theinterplay between effective pairings of (px + py )-type and (px + ipy )-type.Our extensive study paves the way for practically attaining the SOTSC phase byintegrating noncollinear magnetic textures.

Second-order topological superconductor via noncollinear magnetic texture