  Vacuum fluctuation-induced interactions between macroscopic metallic objects
result in an attractive force between them, a phenomenon known as the Casimir
effect. This force is the result of both plasmonic and photonic modes. For very
thin films, field penetration through the films will modify the allowed modes.
Here, we investigate the Casimir interaction between two ultrathin films from
the perspective of the force distribution over real frequencies for the first
time and find pronounced repulsive contributions to the force due to the highly
confined and nearly dispersion-free epsilon-near-zero (ENZ) modes that only
exist in ultrathin films. These contributions are found to persistently occur
around the ENZ frequency of the film and are irrespective of the inter-film
separation. We further associate the ENZ modes with a striking thickness
dependence in the averaged force density for conductive thin films, a metric
signifying a thin-film's acceleration due to Casimir effect. Our results shed
light on the role of the unique vacuum fluctuation modes existing in ultrathin
ENZ materials, which may offer significant potential for engineering the motion
of objects in nanomechanical systems.
