Eur. Phys. J. B (2018) 91: 29
https://doi.org/10.1140/epjb/e2017-80530-8

Regular Article

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

¹ Centre for Advanced Study in Physics, Panjab University, Chandigarh 160014, India
² Department of Physics, MCM DAV College for Women, Chandigarh 160036, India
³ Muenster University of Applied Physics, Stegerwaldstrasse 39, 48565 Steinfurt, Germany
⁴ International Institute of Physics – UFRN, Campus Universitário Lagoa nova, 59078-970 Natal, Brazil
⁵ Max-Planck-Institute for the Physics of Complex Systems, 01187 Dresden, Germany

^a e-mail: morawetz@fh-muenster.de

Received: 16 September 2017
Received in final form: 14 November 2017
Published online: 7 February 2018

Abstract

The structure factor and correlation energy of a quantum wire of thickness b ≪ a_B are studied in random phase approximation (RPA) and for the less investigated region r_s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ϵ_c(b, r_s) = α(r_s)/b + β(r_s) ln(b) + η(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.