Topological defects of spin-orbit coupled Bose-Einstein condensates in a rotating anharmonic trap

We investigate the topological defects and spin structures of binary Bose-Einstein condensates (BECs) with Dresselhaus spin-orbit coupling (D-SOC) in a rotating anharmonic trap. Our results show that for initially mixed BECs without SOC the increasing rotation frequency can lead to the structural phase transition of the system. In the presence of isotropic D-SOC, the system sustains vortex pair,Anderson--Toulouse coreless vortices, circular vortex sheets, and combined vortex structures. In particular, when the rotation frequency is fixed above the radial trapping frequency the strong D-SOC results in a peculiar topological structure which is comprised of multi-layer visible vortex necklaces, hidden vortex necklaces and a hidden giant vortex. In addition, the system exhibits rich spin textures including basic skyrmion, meron cluster, skyrmion string and various skyrmion lattices. The skyrmions will be destroyed in the limit of large D-SOC or rotation frequency. Furthermore, the effects of anisotropic D-SOC and Rashba-Dresselhaus SOC on the topological structures of the system are discussed.