Quantum Effects of Nonlocal Plasmons in Epsilon-Near-Zero Properties of a Thin Gold Film Slab

Dispersion properties of metals and propagation of quantum plasmons in the high photon energy range are studied. The nonlocal dielectric permittivity of a metal is determined by the quantum plasma effects and is calculated by taking into account collisions between free charge carriers and the lattice. The properties of epsilon-near-zero material are investigated in a thin gold film slab. The spectrum and the damping rate of the quantum plasmons are obtained for a wide range of energies, and the electron's wave function is calculated in both classical and quantum limits. It is shown that the quantum plasmons exist with a propagation length of 1-10 nm, which strongly depends on the electron energy. The propagation length is found to be much larger than the propagation length in the classical regime, where the former 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. It is also shown that the damping of electromagnetic waves in the high photon energy range decreases when the photon energy decreases which is opposite to the conclusions obtained from the classical Drude model in this range.