Electronic viscosity in a quantum well: A test for the local density approximation

TL;DR

This paper examines the limitations of the local density approximation in calculating electronic viscosity in quantum wells, revealing significant differences from three-dimensional models and emphasizing the need for improved approximations.

Contribution

It critically compares the effective viscosity in quantum wells with the 3D LDA viscosity, highlighting discrepancies and the necessity for better exchange-correlation functionals.

Findings

Low-frequency shear term dominance differs between models

High-frequency viscosity exhibits different power laws

3D LDA may produce unphysical results in quantum wells

Abstract

In the local density approximation (LDA) for electronic time-dependent current-density functional theory (TDCDFT) many-body effects are described in terms of the visco-elastic constants of the homogeneous three-dimensional electron gas. In this paper we critically examine the applicability of the three-dimensional LDA to the calculation of the viscous damping of 1-dimensional collective oscillations of angular frequency $\omega$ in a quasi 2-dimensional quantum well. We calculate the effective viscosity $\zeta(\omega)$ from perturbation theory in the screened Coulomb interaction and compare it with the commonly used three-dimensional LDA viscosity $Y(\omega)$. Significant differences are found. At low frequency $Y(\omega)$ is dominated by a shear term, which is absent in $\zeta(\omega)$. At high frequency $\zeta(\omega)$ and $Y(\omega)$ exhibit different power law behaviors ($\omega^{-3}$ and $\omega^{-5/2}$ respectively), reflecting different spectral densities of electron-hole excitations in two and three dimensions. These findings demonstrate the need for better approximations for the exchange-correlation stress tensor in specific systems where the use of the three-dimensional functionals may lead to unphysical results.