The inner topological structure and defect control of magnetic skyrmions

The Wu-Yang potential of magnetic skyrmion from SU(2) flat connection

“…∂ µ n i − ig[A µ , n i ] = 0, where A µ = 1 ig ∂ µ U U † is exactly the flat connection as that presented in eq. (18).…”

“…Magnetic skyrmions are a type of quasi-particle that have a vortex-like spin configuration and carry a characteristic topological charge S and are observed in magnetic materials. If Σ is a 2D manifold of 2D magnetic material thin film, we can observe that the skyrmion charge in this film is [18]…”