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Vortex lattice patterns with transitions from regular to other variety vortexshapes are predicted in rotating binary mixtures of dipolar Bose-Einsteincondensates loaded in squared optical lattice. We focus our investigation inthe experimentally accessible dipolar isotopes of dysprosium ($^{162,164}$Dy),erbium ($^{168}$Er), chromium ($^{52}$Cr), and rubidium ($^{87}$Rb), byconsidering the binary mixtures ($^{164}$Dy-$^{162}$Dy, $^{168}$Er-$^{164}$Dy,$^{164}$Dy-$^{52}$Cr and $^{164}$Dy-$^{87}$Rb), which are confined in strongpancake-shaped trap and loaded in squared two-dimensional optical lattices,where we vary the polarization angle of dipoles, the inter-species contactinteractions and the rotation frequency. The ratio between inter- tointra-species contact interaction is used for altering the miscibilityproperties; with the polarization of the dipolar species used for tuning torepulsive or attractive the dipole-dipole interactions. For enough higherrotation, of particular interest is the regime when the inter- to intra-speciesscattering length is larger than one, in which a richer variety ofvortex-lattice patterns are predicted, including vortex sheets andtwo-dimensional rotating droplet formations. The patterns can be controlled bychanging the optical lattice parameters, as shown for the symmetric$^{164}$Dy-$^{162}$Dy dipolar mixture. For mixtures with stronger differencesin the dipole moments, as $^{164}$Dy-$^{52}$Cr and $^{164}$Dy-$^{87}$Rb, onlyhalf quantum vortices and circular ones have been observed, which will dependon the dipole orientations.

Vortex patterns in rotating dipolar Bose-Einstein condensate mixtures with squared optical lattices