Density structures and giant vortex in spin-orbit coupled Bose-Einstein condensates with the harmonic-plus-radial potential

We study the ground-state properties of two-dimensional Bose-Einstein condensate with spin-orbit coupling (SOC) loaded in the harmonic-plus-radial potential. In the immiscible regime, odd-petal-number states can be found. By increasing the effective atom interactions, the odd-petal-number states transform into a phase where petals in the outer annular potential trough are coexisting with inner longitudinal stripes, and finally become the ‘serpentine’ stripe structures. In a rotating system, the giant vortex (GV) can be stabilized and controllable. The favorable conditions for GV are relatively small atom interactions, intermediate rotation frequency and intermediate SOC strength. Further, this type of harmonic-plus-radial trapping with a strong radial part is a suitable choice to create GV state.