Based on the extended Bogoliubov–de Gennes theory, we investigate topological defect states in a time-reversal symmetry-breaking $s+id$ superconductor. In a square lattice hosting two single-quantum vortices along the diagonal, temperature, and intrinsic parameters can drive the splitting of composite vortices into fractional (anti)vortices, giving rise to bow-tie-shaped solitons and skyrmionic chains as well as coreless-type topological excitations. Interestingly, a suitably chosen nonmagnetic impurity near a vortex core induces a skyrmion texture by selectively trapping one single-component vortex, while a magnetic impurity always retains composite vortex structures. In the absence of spin-orbit coupling, the system responds isotropically to Zeeman fields, exhibiting a universal critical field for skyrmion formation. Once spin-orbit interaction is introduced, this response becomes highly anisotropic, with both the critical field strength and the spatial orientation of the resulting skyrmions depending sensitively on the field direction. The simultaneous presence of Rashba and Dresselhaus couplings further reduces the symmetry of the spin-split Fermi surfaces and enables a purely spin-orbit-driven vortex-to-skyrmion transition. In the strong Rashba regime, the system enters a second-order topological superconducting phase, where vortex matter undergoes profound reconstruction as the chemical potential varies. The skyrmion structure emerges at appropriate doping levels, and unique topological defect configurations with fragmented vortex cores are produced upon approaching half filling.

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• Impurities in superconductors
• Vortices in superconductors
• Bogoliubov-de Gennes equations