  We consider the ground-state properties of Rashba spin-orbit-coupled
pseudo-spin-1/2 Bose-Einstein condensates (BECs) in a rotating two-dimensional
(2D) toroidal trap. In the absence of spin-orbit coupling (SOC), the increasing
rotation frequency enhances the creation of giant vortices for the initially
miscible BECs, while it can lead to the formation of semiring density patterns
with irregular hidden vortex structures for the initially immiscible BECs.
Without rotation, strong 2D isotropic SOC yields a heliciform-stripe phase for
the initially immiscible BECs. Combined effects of rotation, SOC, and
interatomic interactions on the vortex structures and typical spin textures of
the ground state of the system are discussed systematically. In particular, for
fixed rotation frequency above the critical value, the increasing isotropic SOC
favors a visible vortex ring in each component which is accompanied by a hidden
giant vortex plus a (several) hidden vortex ring(s) in the central region. In
the case of 1D anisotropic SOC, large SOC strength results in the generation of
hidden linear vortex string and the transition from initial phase separation
(phase mixing) to phase mixing (phase separation). Furthermore, the peculiar
spin textures including skyrmion lattice, skyrmion pair and skyrmion string are
revealed in this system.
