Enhancement of Coulomb blockade in epsilon near zero and hyperbolic metamaterials

Coulomb interaction of charges in a metamaterial may be expressed via its effective dielectric response function. Coulomb interaction appears considerably enhanced in artificially engineered epsilon near zero (ENZ) and hyperbolic metamaterials. Indeed, very recently it was observed that negative ENZ conditions enhance superconducting properties of a composite metamaterial via enhancement of Cooper pairing. Here we demonstrate that positive ENZ conditions enhance Coulomb repulsion of charges, leading to considerable enhancement of the Coulomb blockade effect in such metamaterials. Similar to high Tc cuprates, in hyperbolic metamaterials superconductivity and the Coulomb blockade-induced charge ordering is predicted to compete with each other.