Tunable topological defect states and single-quanta skyrmionic configurations in mesoscopic superconducting rectangular systems with spin-orbit interaction

In the framework of the microscopic Bogoliubov-de Gennes theory, we investigate the topological defect states under out-of-plane magnetic flux in a mesoscopic superconducting rectangular system with spin-orbit (SO) interaction. The $s+id$ superconducting phase with time-reversal symmetry breaking can be realized by suitable choice of model parameters. For the perfect rectangle with pure Dresselhaus SO interaction, the unclosed domain wall carrying two one-component vortices and double-quanta coreless skyrmions can arise stably with increasing flux. Interestingly, when the admixed Rashba SO coupling is included, the evolution of vortex matter toward the single-quanta coreless skyrmion with unit topological charge $Q=1$ favors to take place in the present rectangular system. The relative strength of coupled condensates can be effectively tuned by the strengths of Rashba SO coupling and next-nearest-neighbor hopping, giving rise to rich multiple and hybrid topological defect configurations containing even number of $Q=1$ skyrmions. Moreover, an appropriate in-plane Zeeman potential can drive the splitting of enclosed vortex chains, accompanied with the emergence of obvious single-quanta skyrmionic characters. In particular, the number and location of topological defects are highly sensitive to the surface indentation defect. The single-skyrmionic and multiskyrmionic states consisting of odd number of $Q=1$ skyrmions can also be produced by introducing a defect in the middle of the short or the long edge of the rectangle. Our investigation may shed new light on the single-quanta skyrmions and provide useful information for observing and tuning topological defect states in multicomponent superconducting systems.