Dependence of structure factor and correlation energy on the width of electron wires

TL;DR

This paper investigates how the structure factor and correlation energy of very thin quantum wires depend on their width, providing analytical expressions and comparing with simulation data.

Contribution

It derives analytical formulas for the structure factor and exchange energy of thin quantum wires, especially in the less explored high-density and small-width regime.

Findings

Correlation energy expressed as a function of width and density

Analytical structure factor expressions obtained in random phase approximation

Agreement with quantum Monte Carlo data for practical wire widths

Abstract

The structure factor and correlation energy of a quantum wire of thickness $b\ll a_B$ are studied in random phase approximation and for the less investigated region $r_s<1$. Using the single-loop approximation, analytical expressions of the structure factor have been obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy $\epsilon_c$ is found to be represented by $\epsilon_c (b,r_s)= \frac{\alpha(r_s)}{b} + \beta(r_s)\; ln(b) + \eta(r_s)$, for small $b$ and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.