Renormalization factor and effective mass of the two-dimensional electron gas

TL;DR

This paper investigates the finite-size effects on the momentum distribution, renormalization factor, and effective mass of a two-dimensional electron gas, providing methods to improve convergence to the thermodynamic limit.

Contribution

It introduces an analytical approach to improve the convergence of key properties of the 2D electron gas as system size increases.

Findings

Finite-size corrections scale as N^{-1/4} near the Fermi surface.

The renormalization factor Z is lower than RPA predictions.

The effective mass m* is higher than RPA values.

Abstract

We calculate the momentum distribution of the Fermi liquid phase of the homogeneous, two-dimensional electron gas. We show that, close to the Fermi surface, the momentum distribution of a finite system with $N$ electrons approaches its thermodynamic limit slowly, with leading order corrections scaling as $N^{-1/4}$. These corrections dominate the extrapolation of the renormalization factor, $Z$, and the single particle effective mass, $m^*$, to the infinite system size. We show how convergence can be improved analytically. In the range $1 \le r_s \le 10$, we get a lower renormalization factor $Z$ and a higher effective mass, $m^*>m$, compared to the perturbative RPA values.