Topological defect states in mesoscopic superconductors with mixed pairing symmetries

In the framework of the microscopic Bogoliubov–de Gennes theory, we investigate the vortex and skyrmionic states as well as phase transitions between them in mesoscopic superconducting squares with coexisted spin-triplet (p-wave) and spin-singlet (s-wave and d-wave) pairing symmetries. By choosing different chemical potential $$\mu $$ μ , the influence of next-nearest-neighbor hopping $$t'$$ t ′ on the evolution of mixed pairing orders is mainly discussed. For the case of small $$|\mu |$$ | μ | in which the triplet $$p_{x}\pm {i}p_{y}$$ p x ± i p y -wave symmetry is dominant, the skyrmionic structures containing the vortex-antivortex pair become stable at appropriate external magnetic flux. The transitions between different coreless skyrmionic modes can take place with tuning $$t'$$ t ′ . For further enlarged $$|\mu |$$ | μ | , the singlet s-wave component is gradually enhanced in the present mescoscopic sample. We can obtain the transitions between different multivortex states and between the multivortex and skyrmionic states when $$t'$$ t ′ is varied. The corresponding zero-energy local density of states and the relative phase differences are provided to display different topological defects. Graphic abstract