Quantum phases of rotating Raman spin-orbit-coupled dipolar Bose-Einstein condensates with Lee-Huang-Yang correction

We investigate the ground-state phases and spin textures of rotating binary dipolar Bose-Einstein condensates with Lee-Huang-Yang (LHY) correction and Raman-induced spin-orbit coupling (SOC) in a harmonic trap. Without rotation and SOC, the enhanced LHY correction can lead to structural phase transitions of the system. In the presence of SOC, a phase diagram as a function of the Raman coupling and LHY correction strengths is given. It is shown that the system exhibits rich and exotic quantum phases including quantum droplet (QD) phase with hidden vortex-antivortex pairs, droplet-stripe coexistence phase with hidden vortex-antivortex cluster, QD phase with visible triangular vortex lattice, annular stripe phase containing Anderson-Toulouse coreless vortex, and annular phase with vortex-antivortex pair necklace. In particular, for the rotation case, with the variation of Raman coupling strength the system displays complicated ground-state structures, such as layered structure of droplet necklaces and annular stripe with hidden layered vortex necklace and antivortex necklace, toroidal stripe phase with hidden antivortex necklace, and composite phase of visible square antivortex lattice and annular stripe. Furthermore, the system sustains fascinating novel spin textures and skyrmion excitations, including triangular half-antiskyrmion lattice, alternating meron-antimeron necklace, double-layer half-skyrmion necklace, and triangular half-skyrmion lattice.