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 $\omega$ 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.

10 pages, 7 figures, RevTex4

References in corpus (11)

• Current-dependent exchange-correlation potential for dynamical linear response theory
• Time-dependent density functional theory beyond the adiabatic local density approximation
• Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems
• The Elasticity of an Electron Liquid
• Stochastic Time-Dependent Current-Density-Functional Theory
• Time-dependent current density functional theory for the linear response of weakly disordered systems
• Microscopic Current Dynamics in Nanoscale Junctions
• Local electron heating in nanoscale conductors
• Time-dependent Kohn-Sham theory with memory
• Relaxation in time-dependent current-density functional theory
• Hydrodynamic approach to transport and quantum turbulence in nanoscale conductors

Cited by in corpus (6)

• Towards a dynamical approach to the calculation of the figure of merit of thermoelectric nanoscale devices
• Three- to two-dimensional crossover in time-dependent density-functional theory
• Local electron and ionic heating effects on the conductance of nanostructures
• Turbulence-induced magnetic flux asymmetry at nanoscale junctions
• Chirality and intrinsic dissipation of spin modes in two-dimensional electron liquids
• Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results