  The competition between tunneling and interactions in bosonic lattice models
generates a whole variety of different quantum phases. While, in the presence
of a single species interacting via on-site interaction, the phase diagram
presents only superfluid or Mott insulating phases, for long-range interactions
or multiple species, exotic phases such as supersolid (SS) or pair-superfluid
(PSF) appear. In this work, we show for the first time that the co-existence of
effective multiple species and long-range interactions leads to the formation
of a novel pair-supersolid (PSS) phase, namely a supersolid of composites. We
propose a possible implementation with dipolar bosons in a bilayer
two-dimensional optical lattice.
