  Single-layer graphene sheets are typically characterized by long-wavelength
corrugations (ripples) which can be shown to be at the origin of rather strong
potentials with both scalar and vector components. We present an extensive
microscopic study, based on a self-consistent Kohn-Sham-Dirac
density-functional method, of the carrier density distribution in the presence
of these ripple-induced external fields. We find that spatial density
fluctuations are essentially controlled by the scalar component, especially in
nearly-neutral graphene sheets, and that in-plane atomic displacements are as
important as out-of-plane ones. The latter fact is at the origin of a
complicated spatial distribution of electron-hole puddles which has no evident
correlation with the out-of-plane topographic corrugations. In the range of
parameters we have explored, exchange and correlation contributions to the
Kohn-Sham potential seem to play a minor role.
