Spin-orbit coupling controlling the topological vortical phase transition in spin-2 rotating Bose-Einstein condensates

We investigate the combined effects of spin-orbit coupling and rotation on the topological vortical phase transition in F = 2 Bose-Einstein condensates. We find that the spin-orbit coupling can precisely manipulate the canonical atom current which is generated in the opposite direction of the gauge atom current and causes both a continuous and a discontinuous canonical angular momentum. We apply the canonical angular momentum and magnetization to reveal the emergence of novel topological excitations, such as the Anderson-Toulouse vortex as well as the vortex-dipole lattice. Especially, strong spin-orbit coupling can induce two perpendicular vortex chains. We also find that both the first-order and the second-order phase transition can be characterized by the canonical angular momentum and the magnetization. Differently from the spin singlet-pairing interaction, the spin-exchange interaction can adjust the canonical angular momentum and control the phase transition well. The topological vortical phase transition in an F = 2 cold-atom system is compatible with the current experiment and can be detected by the spin polarization procedure.