Electrically induced charge-density waves in a two-dimensional electron channel: Beyond the Local Density Approximation

TL;DR

This paper refines the calculation of charge-density wave formation in a 2D electron gas by including gradient corrections, revealing a lower critical density for wave onset consistent with stability analysis.

Contribution

It introduces a self-consistent gradient correction to the energy calculation, improving the prediction of charge-density wave onset in 2D electron channels.

Findings

Lower critical density for charge density wave formation.

Agreement between energy-based and stability analysis results.

Enhanced understanding of density variations in 2D electron gases.

Abstract

In a previous paper we suggested that a macroscopic force field applied across a two-dimensional electron gas channel could induce a microscopic charge density wave as soon as the proper compressibility becomes negative, which happens at densities much higher than the critical density for the Wigner crystal transition. The suggestion was based on a calculation of the ground state energy in the local density approximation. In this paper we refine our calculation of the energy by including a self-consistent gradient correction to the kinetic energy. Due to the increased energy cost of rapid density variations, we find a much lower critical density for the onset of the charge density wave. This critical density coincides with the result of a linear stability analysis of the uniform ground state in the absence of the electric field.