  The recent realization of binary dipolar BEC [Phys. Rev. Lett. 121, 213601
(2018)] opens new exciting aspects for studying quantum droplets and
supersolids in a binary mixture. Motivated by this experiment, we study
groundstate phases and dynamics of a Dy-Dy mixture. Dipolar bosonic mixture
exhibits qualitatively novel and rich physics. Relying on the three-dimensional
numerical simulations in the extended Gross-Pitaevskii framework, we unravel
the groundstate phase diagrams and characterize different groundstate phases.
The emergent phases include both miscible and immiscible single droplet (SD),
multiple droplets (MD), supersolid (SS), and superfluid (SF) states. More
intriguing mixed groundstates may occur for an imbalanced binary mixture,
including a combination of SS-SF, SS-MD, and SS-SS phases. We observed the
dynamical transition from a miscible MD state to an immiscible MD state with
multiple domains formed along the axial direction by tuning the inter-species
scattering length. Also by linear quenches of intra-species scattering lengths
across the aforementioned phases, we monitor the dynamical formation of
supersolid clusters and droplet lattices. Although we have demonstrated the
results for a Dy-Dy mixture and for a specific parameter range of intra-species
and inter-species scattering lengths, our results are generally valid for other
dipolar mixtures and may become an important benchmark for future experimental
scenarios.
