  In three-dimensional materials with a Dirac spectrum, weak short-ranged
disorder is essentially irrelevant near the Dirac point. This is manifestly not
the case for Coulomb disorder, where the long-ranged nature of the potential
produced by charged impurities implies large fluctuations of the disorder
potential even when impurities are sparse, and these fluctuations are screened
by the formation of electron/hole puddles. In this paper I present a theory of
such nonlinear screening of Coulomb disorder in three-dimensional Dirac
systems, and I derive the typical magnitude of the disorder potential, the
corresponding density of states, and the size and density of electron/hole
puddles. The resulting conductivity is also discussed.

Disordered Systems and Neural Networks;Mesoscale and Nanoscale Physics