Sabine Hossenfelder has this interesting post on Backreaction about the Casimir effect here. She speculates that the effect will be manifest in carbon nanotubes. Her other thought is that the energy density (effective mass) within the nanotube would be negative -- so how would this couple to gravity? Would there be an antigravity effect?
Lacking a proper theory of quantum gravity, it appears difficult to work this out. I wonder whether a similar effect could be expected in the lattice of a metallic crystal?