Three- to two-dimensional crossover in time-dependent density-functional theory

TL;DR

This paper investigates the transition from three-dimensional to two-dimensional behavior in time-dependent density-functional theory, focusing on the performance of various exchange kernels in quantum wells as they approach the 2D limit.

Contribution

It provides a comparative analysis of local, semilocal, and orbital-dependent exchange kernels in the dynamical regime for quasi-2D systems, highlighting their limitations.

Findings

3D (semi)local exchange functionals fail near the 2D limit at low densities.

3D local exchange remains valid for typical quantum well parameters except at very low densities.

The study clarifies the applicability of exchange functionals in quasi-2D dynamical systems.

Abstract

Quasi-two-dimensional (2D) systems, such as an electron gas confined in a quantum well, are important model systems for many-body theories. Earlier studies of the crossover from 3D to 2D in ground-state density-functional theory showed that local and semilocal exchange-correlation functionals which are based on the 3D electron gas are appropriate for wide quantum wells, but eventually break down as the 2D limit is approached. We now consider the dynamical case and study the performance of various linear-response exchange kernels in time-dependent density-functional theory. We compare approximate local, semilocal and orbital-dependent exchange kernels, and analyze their performance for inter- and intrasubband plasmons as the quantum wells approach the 2D limit. 3D (semi)local exchange functionals are found to fail for quantum well widths comparable to the 2D Wigner-Seitz radius, which implies in practice that 3D local exchange remains valid in the quasi-2D dynamical regime for typical quantum well parameters, except for very low densities.