Vortex lattices in binary Bose-Einstein condensates with dipole-dipole interactions

We study the structure and stability of vortex lattices in two-component rotating Bose-Einstein condensates with intrinsic dipole-dipole interactions (DDIs) and contact interactions. To address experimentally accessible coupled systems, we consider $^{164}$Dy-$^{162}$Dy and $^{168}$Er-$^{164}$Dy mixtures, which feature different miscibilities. The corresponding dipole moments are $\mu_{\mathrm{Dy}}=10\mu_{\mathrm{B}}$ and $\mu_{\mathrm{Er}}= 7\mu_{\mathrm{B}}$, where $\mu_{\mathrm{B}}$ is the Bohr magneton. For comparison, we also discuss a case where one of the species is non dipolar. Under a large aspect ratio of the trap, we consider mixtures in the pancake-shaped format, which are modeled by effective two-dimensional coupled Gross-Pitaevskii equations, with a fixed polarization of the magnetic dipoles. Then, the miscibility and vortex-lattice structures are studied, by varying the coefficients of the contact interactions (assuming the use of the Feshbach-resonance mechanism) and the rotation frequency. We present phase diagrams for several types of lattices in the parameter plane of the rotation frequency and ratio of inter- and intra-species scattering lengths. The vortex structures are found to be diverse for the more miscible $^{164}$Dy-$^{162}$Dy mixture, with a variety of shapes, whereas, for the less miscible case of $^{168}$Er-$^{164}$Dy, the lattice patterns mainly feature circular or square formats.