Vortex Phase Transitions And Skyrmions In The Cooper-Oxide Superconductor With Coupled S-and D-Wave Pairings

We investigate phase transitions of vortex states by minimizing the microscopic Ginzburg-Landau free energy functional for the copper-oxide superconductors with mixed spin singlet s-and d-wave condensates.It is found that the vortex phase transition occurs from the conventional Abrikoso vortex to a semi-vortex with spatially separated s-and d-wave cores as the temperature cooling down.Skyrmion modes with nontrivial topological charge are revealed in relating to the semi-vortex phase.Interestingly,both the Skyrmion texture and the topological charge are tunable with an external applied magnetic field.We explain that phase separation and the Skyrmion mode of topologically non-trivial are possible when there presents couplings between the two condensates of different symmetry in the model.In present case,the inter-channel orbit coupling exerts an opposite orbit effective field to different pairing channels and allows local time-reversal violating bound state,since a successive operation in the orbital parity(P)and the time-reversal(T)obeys PT = +1 for the spin-singlet pairing states.