Linear Response and the Thomas-Fermi Approximation in Undoped Graphene

TL;DR

This paper evaluates the applicability of Thomas-Fermi theory for modeling charge density variations in neutral graphene, finding linear response theory more accurate for typical experimental conditions.

Contribution

It compares exact tight-binding results with linear response and Thomas-Fermi approximations to determine their validity ranges in undoped graphene.

Findings

Linear response outperforms Thomas-Fermi in accuracy for relevant experimental parameters.

Thomas-Fermi theory is less accurate for small length scales and low densities.

Linear response provides a better description of charge modulations in neutral graphene.

Abstract

We analyze the range of validity of Thomas Fermi theory for describing charge density modulations induced by external potentials in neutral graphene. We compare exact results obtained from a tight-binding calculation with those of linear response theory and the Thomas Fermi approximation. For experimentally interesting ranges of size and density amplitudes (electron densities less than $\sim 10 ^{11} cm ^{-2}$, and spatial length scales below $\sim 20 nm$), linear response is significantly more accurate than Thomas Fermi theory.