Optical conductivity of metal nanofilms and nanowires: The rectangular-box model

TL;DR

This paper models the optical conductivity of ultrathin metal nanofilms and nanowires using a particle-in-a-box approach, revealing size-dependent oscillations and frequency effects that align with experimental data.

Contribution

It introduces a conductivity tensor for low-dimensional systems and provides analytical estimations of size effects and Fermi level oscillations in ultrathin metal nanostructures.

Findings

Size and frequency strongly influence conductivity components.

Oscillations of Fermi energy depend on system size.

Differences in relaxation times explain material-specific results.

Abstract

The conductivity tensor is introduced for the low-dimensional electron systems. Within the particle-in-a-box model and the diagonal response approximation, components of the conductivity tensor for a quasi-homogeneous ultrathin metal film and wire are calculated under the assumption $d\cong \lambda_{\rm F}$ (where $d$ is the characteristic small dimension of the system, $\lambda_{\rm F}$ is the Fermi wavelength for bulk metal). We find the transmittance of ultrathin films and compare these results with available experimental data. The analytical estimations for the size dependence of the Fermi level are presented, and the oscillations of the Fermi energy in ultrathin films and wires are computed. Our results demonstrate the strong size and frequency dependences of the real and imaginary parts of the conductivity components in the infrared range. A sharp distinction of the results for Au and Pb is observed and explained by the difference in the relaxation time of these metals.