Vortex structures in a rotating Rydberg-dressed Bose-Einstein condensate with the Lee-Huang-Yang correction

We numerically investigate the vortex structures in a fast rotating two-dimensional Rydberg-dressed Bose-Einstein condensate (BEC) taking into account the Lee-Huang-Yang (LHY) quantum correction. In a rotating BEC of reduced dimensionality, it is shown that there is room to tune the LHY coupling against the short- and long-range couplings. In the absence of the LHY effect, hexagonal, square, striped, and honeycomb lattices can exhibit upon increasing the long-range interaction, which can be realized in the context of superfluid (SF)-supersolid (SS) transition. In the presence of the LHY effect, competition between LHY and long-range terms results in rich lattice structures. In particular, clustering of multiple vortices can occur due to the trapping effect of the SS triangles or grids. Estimates of number of vortices in the clustering are provided.