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 and contact interactions. To address experimentally accessible coupled systems, we consider Dy-164-Dy-162 and Er-168-Dy-164 mixtures, which feature different miscibilities. The corresponding dipole moments are mu(Dy) = 10 mu(B) and mu(Er) = 7 mu(B), where mu(B) is the Bohr magneton. For comparison we also discuss a case where one of the species is nondipolar. 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 the ratio of inter-and intraspecies scattering lengths. The vortex structures are found to be diverse for the more miscible Dy-164-Dy-162 composition, with a variety of shapes, whereas for the less miscible case of Er-168-Dy-164, the lattice patterns mainly feature circular or square formats.