  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.
