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

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 $ω$ in a quasi 2-dimensional quantum well. We calculate the effective viscosity $ζ(ω)$ from perturbation theory in the screened Coulomb interaction and compare it with the commonly used three-dimensional LDA viscosity $Y(ω)$. Significant differences are found. At low frequency $Y(ω)$ is dominated by a shear term, which is absent in $ζ(ω)$. At high frequency $ζ(ω)$ and $Y(ω)$ exhibit different power law behaviors ($ω^{-3}$ and $ω^{-5/2}$ 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.