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 $\ensuremath{\sim}{10}^{11}\text{ }{\text{cm}}^{\ensuremath{-}2}$, and spatial length scales below $\ensuremath{\sim}20\text{ }\text{nm}$), linear response is significantly more accurate than Thomas-Fermi theory.
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