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Spin-Orbit Coupled Bose-Einstein Condensate under Rotation

We examine the combined effects of Rashba spin-orbit (SO) coupling and rotation on trapped spinor Bose-Einstein condensates (BECs). Nature of single particle states is thoroughly examined in the Landau level basis and is shown to support the formation of half-quantum vortex. In the presence of weak s-wave interactions, the ground state at strong SO coupling develops ring-like structures with domains whose number shows step behavior with increasing rotation. For fast rotation case, the vortex pattern favors triangular lattice, accompanied by the density depletion in the central region and weakened Skyrmionic character as the SO coupling is enhanced. Giant vortex formation is facilitated when SO coupling and rotation are both strong.