Quantum plasmon effects in epsilon-near-zero metamaterials

Dispersion properties of metals and propagation of quantum bulk plasmon in the high photon energy regime are studied. The nonlocal dielectric permittivity of a metal is determined by the quantum plasma effects and is calculated by applying the Wigner equation in the kinetic theory and taking into account the electron lattice collisions. The properties of epsilon near zero material are investigated in a thin gold film. The spectrum and the damping rate of the quantum bulk plasmon are obtained for a wide range of energies, and the electron wave function is analytically calculated in both classical and quantum limits. It is shown that the quantum bulk plasmons exist with a propagation length of 1 to 10nm, which strongly depends on the electron energy. The propagation length is found to be much larger than the propagation length in the classical regime which is comparable to the atomic radius and the average inter particle distance. It is found that the spatial localization of the electron wave function is extended due to the quantum effects. Also, it is shown that the damping of electromagnetic waves decreases when the energy of the photon decreases which is opposite to the conclusions obtained from the classical Drude model. The importance of the quantum effects in the development of next-generation metamaterials is also discussed.