Linear Response and the Thomas-Fermi Approximation in Undoped Graphene

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.