Continuous topological transition from metal to dielectric

Metal and dielectric have long been thought as two different states of matter possessing highly contrasting electric and optical properties. A metal is a material highly reflective to electromagnetic waves for frequencies up to the optical region. In contrast, a dielectric is transparent to electromagnetic waves. These two different classical electrodynamic properties are distinguished by different signs of the real part of permittivity: The metal has a negative sign while the dielectric has a positive one. Here, we propose a different topological understanding of metal and dielectric. By considering metal and dielectric as just two limiting cases of a periodic metal–dielectric layered metamaterial, from which a metal can continuously transform into a dielectric by varying the metal filling ratio from 1 to 0, we further demonstrate the abrupt change of a topological invariant at a certain point during this transition, classifying the metamaterials into metallic state and dielectric state. The topological phase transition from the metallic state to the dielectric state occurs when the filling ratio is one-half. These two states generalize our previous understanding of metal and dielectric: The metamaterial with metal filling ratio larger/smaller than one-half is named as the “generalized metal/dielectric.” Interestingly, the surface plasmon polariton (SPP) at a metal/dielectric interface can be understood as the limiting case of a topological edge state.