  In an ideal graphene sheet charge carriers behave as two-dimensional (2D)
Dirac fermions governed by the quantum mechanics of massless relativistic
particles. This has been confirmed by the discovery of a half-integer quantum
Hall effect in graphene flakes placed on a SiO2 substrate. The Dirac fermions
in graphene, however, are subject to microscopic perturbations that include
topographic corrugations and electron density inhomogeneities (i.e. charge
puddles). Such perturbations profoundly alter Dirac fermion behavior, with
implications for their fundamental physics as well as for future graphene
device applications. Here we report a new technique of Dirac point mapping that
we have used to determine the origin of charge inhomogeneities in graphene. We
find that fluctuations in graphene charge density are not caused by
topographical corrugations, but rather by charge-donating impurities below the
graphene. These impurities induce unexpected standing wave patterns due to
supposedly forbidden back-scattering of Dirac fermions. Such wave patterns can
be continuously modulated by electric gating. Our observations provide new
insight into impurity scattering of Dirac fermions and the microscopic
mechanisms limiting electronic mobility in graphene.
