Gap-Size-Dependent Effective Phase Transition in Metasurfaces of Closed-Ring Resonators

We theoretically investigate a metal-to-insulator transition in artificial two-dimensional (2D) crystals (i.e., metasurfaces) of tightly coupled closed-ring resonators. Strong interaction between unit resonators the metasurfaces yields effective permittivity highly dependent on lattice spacing Through our rigorous theory, we provide closed form metasurface and reveal that possesses Lorentzian-type resonant behavior, implying can arise when passes critical value.