  There is a growing interest in using cold-atom systems to explore the effects
of strong interactions in topological band structures. Here we investigate
interacting bosons in a Cruetz ladder, which is characterised by topological
flat energy bands where it has been proposed that interactions can lead to the
formation of bound atomic pairs giving rise to pair superfluidity. By
investigating realistic experimental implementations, we understand how the
lattice topology enhances the properties of bound pairs giving rise to
relatively large effective pair-tunnelling in these systems which can lead to
robust pair superfluidity, and we find lattice supersolid phases involving only
pairs. We identify schemes for preparation of these phases via time-dependent
parameter variation and look at ways to detect and characterise these systems
in a lattice. This work provides a starting point for investigating the
interplay between the effects of topology, interactions and pairing in more
general systems, with potential future connections to quantum simulation of
topological materials.
