Dielectric tensor of low-dimensional metal systems

Surface plasmon polaritons in dielectric/metal/dielectric structures: metal layer thickness influence

“…As a model for the dielectric function ε 2 (q, z, z ′ , ω) of the metal layer, we will use the diagonal component of the dielectric permittivity tensor of a metal film which is obtained in [7],…”

“…Here ω p = 4πn e e 2 /m e is the plasma frequency [1,4], n e is an electron density in a metal, f n = Θ(ε n − ε F ) is the Fermi-Dirac function [7,8], Θ(x) is the Heaviside step function [8], ε F is the Fermi energy [4,8], r = (r || , z).…”

“…Square brackets indicate taking the integer part. Expression for ε(q, z, z ′ , ω) (7) for the model (15) has the form (for details see [7])…”

SPP waves in "dielectric-metal-dielectric" structures: influence of exchange correlations

“…Under such assumptions we are neglecting the dispersion ε 2 and σ 2 along OZ, which is, generally speaking, true for metal films with the thickness 2δ that satisfies the condition 2δk F ∼ 1 ÷ 10, where k F = ( 3 4π ) 2 3 r s a −1 0 , r s is Gell-Mann-Brakner parameter, a 0 is Bohr raduis [6,7] and the influence of fringe effects in the XOY plane (this is true when geometric dimensions of a metal film in XOY are considerably larger than its thickness along OZ, 2δ( √ S) −1 ≪ 1, where S is an area of the metal film surface).…”

“…State-of-art approaches to mathematical modeling of propagation of SPP waves are based on the classical Drude theory [2,3] which, as is known [4,5], does not consider spatial dispersion of metal dielectric permittivity ε(r, t) and effects caused by the interaction of electrons in a metal layer. Those effects become especially significant (and in the same time complicated for modeling) in a low-scale (nanoscale) metallic systems which are used in "dielectric-metal-dielectric" structures (DMD structures) synthesis [6,7].…”