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 similar to 10(11) cm(-2), and spatial length scales below similar to 20 nm), linear response is significantly more accurate than Thomas-Fermi theory.