Tunable Casimir Repulsion with Three-Dimensional Topological Insulators

In this Letter, we show that switching between repulsive and attractive Casimir forces by means of external tunable parameters could be realized with two topological insulator plates. We find two regimes where a repulsive (attractive) force is found at small (large) distances between the plates, canceling out at a critical distance. For a frequency range where the effective electromagnetic action is valid, this distance appears at length scales corresponding to $1\ensuremath{-}ϵ(\ensuremath{\omega})\ensuremath{\sim}(2/\ensuremath{\pi})\ensuremath{\alpha}\ensuremath{\theta}$.