Skyrmionic configuration and half-quantum vortex-antivortex pair in mesoscopic p -wave superconducting noncircular systems

In the framework of the microscopic Bogoliubov-de Gennes theory, we study the topological properties of skyrmionic states under applied magnetic flux in mesoscopic symmetric and asymmetric $p$-wave superconducting noncircular systems. For a perfect square (rectangular) sample, an enclosed square-loop-like (parallelogram-loop-like) chain comprising four spatially separated one-component vortices emerges for a single-skyrmion state with the topological charge $Q=2$. A multiskyrmion state containing two concentric skyrmions can be found in the square case, and more complex skyrmionic structures with $Q>2$ take place when the superconducting pairing interaction becomes stronger. By contrast, the mesoscopic rectangular geometry favors different arrangements of skyrmions. A novel type of multiskyrmion states with two or three separated skyrmions aligning along the long side of the rectangle becomes stable, accompanied with the half-quantum vortex-antivortex (V-Av) pair in one component of the order parameter. Moreover, for the square loops with a small square hole, the singly quantized vortex always traps in the centered or off-centered hole, while the coreless skyrmion located in the superconducting region tries to restore the centrally symmetric character. For some critical displacement of the off-centered hole, the half-quantum V-Av pair can occur in such asymmetric system.