  We study the ground-state properties of dipolar spin-1/2 Bose-Einstein
condensates with quantum fluctuations and Rashba spin-orbit coupling (SOC). The
combined effects of dipole-dipole interaction (DDI), SOC, and Lee-Huang-Yang
(LHY) correction induced by quantum fluctuations on the ground-state structures
and spin textures of the system are analyzed and discussed. For the nonrotating
case and fixed nonlinear interspecies contact interaction strengths, our
results show that structural phase transitions can be achieved by adjusting the
strengths of the DDI and LHY correction. In the absence of SOC, a ground-state
phase diagram is given with respect to the DDI strength and the LHY correction
strength. We find that the system exhibits rich quantum phases including square
droplet lattice phase, annular phase, loop-island structure, stripe-droplet
coexistence phase, toroidal stripe phase, and Thomas-Fermi (TF) phase. For the
rotating case, the increase of DDI strength can lead to a quantum phase
transition from superfluid phase to supersolid phase. In the presence of SOC,
the quantum droplets display obvious stretching and hidden vortex-antivortex
clusters are formed in each component. In particular, weak or moderate SOC
favors the formation of droplets while for strong SOC the ground state of the
system develops into a stripe phase with hidden vortex-antivortex clusters.
Furthermore, the system sustains exotic spin textures and topological
excitations, such as composite skyrmion-antiskyrmion-meron-antimeron cluster,
meron-antimeron string cluster, antimeron-meron-antimeron chain cluster, and
peculiar skyrmion-antiskyrmion-meron-antimeron necklace with a meron-antimeron
necklace embedded inside and a central spin Neel domain wall.
