Mechanisms for Magnetic Skyrmion Catalysis and Topological Superconductivity

We propose an alternative route to stabilize magnetic skyrmion textures, which is free from the requirement of Dzyaloshinkii-Moriya interaction, magnetic anisotropy and the application of an external Zeeman field. Instead, it solely relies on time reversal symmetry (TRS) violation, and the emergence of flux in the ground state. We discuss scenarios that lead to a nonzero flux, and identify the possible magnetic ground states which become accessible in its presence. We focus on itinerant magnets with tetragonal symmetry, which preserve the full spin-rotational group but violate TRS. We demonstrate our mechanism for a concrete extended Dirac model, which can describe the protected surface states of a topological crystalline insulator. In addition, we investigate the topological phases obtained for the above extended Dirac model when two distinct magnetic skyrmion crystal ground states coexist with a conventional pairing gap. We find chiral topological superconducting phases, which harbor an integer number of chiral Majorana modes when line defects are present. Our mechanism opens alternative perspectives for engineering topological superconductivity in a minimal fashion. Evenmore, relaxing the stringent requirements to generate skyrmions, also promises to unlock new functional topological materials and devices which may be more compatible with electrostatic control than the currently explored skyrmion-Majorana platforms.