  The Casimir force is a universal interaction induced by electromagnetic
quantum fluctuations between any types of objects. The expansion of the
graphene family by adding silicene, germanene, and stanene, 2D allotropes of
Si, Ge, and Sn, lands itself as a platform to probe Dirac-like physics in
honeycomb staggered systems in such a ubiquitous interaction. We discover
Casimir force phase transitions between these staggered 2D materials induced by
the complex interplay between Dirac physics, spin-orbit coupling, and
externally applied fields. In particular, we find that the interaction energy
experiences different power law distance decays, magnitudes, and dependences on
characteristic physical constants. Furthermore, due to the topological
properties of these materials, repulsive and quantized Casimir interactions
become possible.
