Spin and temperature dependent study of exchange and correlation in thick two-dimensional electron layers

TL;DR

This study investigates how exchange and correlation energies in finite-width 2D electron layers depend on density, spin polarization, and temperature, using pair-distribution functions and an approximation method to interpolate between 1D and 3D behaviors.

Contribution

The paper introduces a constant-density approximation to analyze exchange-correlation effects in quasi-2D electron layers, accounting for finite width and strong correlations.

Findings

Correlation energy varies with layer width and density

Transition to spin-polarized phase characterized

Effective mass and g-factor affected by parameters

Abstract

The exchange and correlation $E_{xc}$ of strongly correlated electrons in 2D layers of finite width are studied as a function of the density parameter $r_s$, spin-polarization $\zeta$ and the temperature $T$. We explicitly treat strong-correlation effects via pair-distribution functions, and introduce an equivalent constant-density approximation (CDA) applicable to all the inhomogeneous densities encountered here. The width $w$ defined via the CDA provides a length scale defining the $z$-extension of the quasi-2D layer resident in the $x$-$y$ plane. The correlation energy $E_c$ of the quasi-2D system is presented as an interpolation between a 1D gas of electron-rods (for $w/r_s>1$) coupled via a log(r) interaction, and a 3D Coulomb fluid closely approximated from the known {\it three-dimensional} correlation energy when $w/r_s$ is small. Results for the $E_{xc}(r_s,\zeta,T)$, the transition to a spin-polarized phase, the effective mass $m^*$, the Land\'e $g$-factor etc., are reported here.