Nanoscale physics

The influence of Coulomb interaction on the frequency spectrum of surface plasmons in dielectric/metal/dielectric structures 
Kostrobij P.P.1, Markovych B.M.1, Polovyi V.Ye.1
1 Lviv Polytechnic National University. Stepana Bandery St, 12, Lviv, Lviv Oblast, 79000, Ukraine. 
E-mail: vitalii.y.polovyi@lpnu.ua

In our previous works [1,2], we studied the dependence of dielectric permittivity function on a thickness of a metal layer and the influence of the condition of electroneutrality [3] for an asymmetric rectangular potential well of a finite depth and found that the condition of electroneutrality for small thicknesses gives a shift of oscillation peaks with a general tendency towards an attenuation in the plasmon frequency peaks compared with the case when a wave vector depends only on an average concentration of electrons in a metal. Alas, in both cases the influence on the frequency spectrum of SPPs waves was relatively small. Therefore in this work, we propose additionally to take into account Coulomb interaction between electrons in a metal layer and to study its influence on the spectrum through the effect of this interaction on the chemical potential [3] 
The simulation results show that for atomically thin metal films (ATFM) Coulomb interaction has a significant effect on the behavior of a frequency spectrum. Moreover, obtained results better agree with an experimental data [4].

1.	P. Kostrobij, V. Polovyi. Influence of the Thickness of a Metal Nanofilm on the Spectrum of Surface Plasmons. // MMC.-2019.-Vol. 6, N 1.-P. 109-115.
2.	P. Kostrobij, V. Polovyi. Influence of the Electroneutrality of a Metal Layer on the Plasmon Spectrum in Dielectric-Metal-Dielectric structures // MMC.-2019.-Vol 6, N 2.-P. 297–303.
3.	P. Kostrobij, B. Markovych. The chemical potential and the work function of a metal film on a dielectric substrate // Phil. Mag. Letters.-2019.-P.12-20.
4.	M. Abd El-Fattah, Zakaria, Mkhitaryan, Vahagn, Brede, et al. Plasmonics in Atomically-Thin Crystalline Silver Films // ACS Nano. 13. 10.1021/acsnano.9b0165.-2019.