Repulsive, nonmonotonic Casimir forces in a glide-symmetric geometry

We describe a three-dimensional geometry that exhibits a repulsive Casimir force using ordinary metallic materials, as computed via an exact numerical method (no uncontrolled approximations). The geometry consists of a zippelike, glide-symmetric structure formed of interleaved metal brackets attached to parallel plates. Depending on the separation, the perpendicular force between the plates/brackets varies from attractive (large separations) to repulsive (intermediate distances) and back to attractive (close separations), with one point of stable equilibrium in the perpendicular direction. This geometry was motivated by a simple intuition of attractive interactions between surfaces, and so we also consider how a rough proximity force approximation of pairwise attractions compares to the exact calculations.