  We study the repulsive-attractive transition, regarded as stable equilibrium,
between gold and dielectric metamaterial based on Mie resonance immersed in
various fluids due to the interplay of gravity, buoyancy and Casimir force
among different geometries consisting of parallel plates and spheres levitated
over substrates. A wider range of separation distance of stable equilibrium is
obtained with Mie metamaterial than natural materials. We investigate the
relationship between separation distance of stable equilibrium and constructive
parameters of Mie metamaterial and geometric parameters of the system, and
provide simple rules to tune the equilibrium position by modifying constructive
parameters of Mie metamaterial. Particularly, the effect of permeability of Mie
metamaterial on equilibrium separation is also considered. Our work is
promising for potential applications in frictionless suspension in
micro/nanofabrication technologies.
