Ab initio theory of the Drude plasma frequency

TL;DR

This paper develops a quantum mechanical framework to accurately compute the Drude plasma frequency tensor, accounting for material anisotropy and strain effects, and validates it against noble metal experiments.

Contribution

It introduces a first-principles method to calculate the Drude tensor, extending the classical plasma frequency concept to anisotropic and strained metallic systems.

Findings

The Drude tensor generalizes the plasma frequency to anisotropic materials.

Results for Cu, Ag, Au match experimental data.

Strain effects on plasma frequency are quantitatively analyzed.

Abstract

We derive a theoretical expression to calculate the Drude plasma frequency $\omega_p$ based on quantum mechanical time dependent perturbation theory. We show that in general $\omega_p^2$ should be replaced by a second rank tensor, the Drude tensor $\mathcal{D}$, which we express in terms of products of the velocity expectation values integrated over the Fermi surface, and which is amiable to analytical and numerical evaluation. For the Sommerfeld's model of metals our expression yields the ubiquitous plasma frequency $\omega^2_p=4\pi n_e e^2/m_e$. The Drude tensor takes into account the geometry of the unit cell and may be calculated from first principles for isotropic as well as anisotropic metallic systems. We present results for the noble metals, Cu, Ag, and Au without stress and subject to isotropic and uniaxial strains, and we compare the results to those available from experiment.