Single half-skyrmion chain in spin-orbit-coupled toroidal Bose-Einstein condensate with gradient magnetic field

The ground-state properties of a spin-orbit-coupled rotating Bose-Einstein condensate with a gradient magnetic field in a toroidal trap are studied. When gradient magnetic fields are taken into account, the results are quite novel in that, in the spin-orbit-coupled nonrotating Bose-Einstein condensate with small gradient magnetic field intensity, the ferromagnetic system presents a plane-wave phase and satisfies the translational symmetry, and the antiferromagnetic system presents a stripe phase. With the increase of the magnetic field intensity, the translational symmetry of the ground state of the ferromagnetic system is broken, and the phase change tends to be similar in both ferromagnetic and antiferromagnetic systems. Considering the spin-orbit-coupled rotating Bose-Einstein condensate, the system gradually transforms from the nonsingle half-skyrmion chain to the single half-skyrmion chain with the increase of the gradient magnetic field, while the single half-skyrmion chain transforms to the nonsingle half-skyrmion chain with the increase of spin-orbit coupling. In addition, we obtain the phase diagram as a function of the gradient magnetic field and the spin-orbit-coupling intensity.