  This thesis studies how the rudimentary attributes of graphene's charge
carriers, and local moments on its surface, can be directly manipulated and
controlled with electrostatic potentials. We first consider bilayer graphene
subject to a spatially varying electrostatic potential that forms two
neighbouring regions with opposite interlayer bias. Along the boundary, 1D
chiral "kink" states emerge. We find that these 1D modes behave as a strongly
interacting Luttinger liquid whose properties can be tuned via an external
gate. Next, we consider superlattices in bilayer graphene. Superlattices are
seen to have a more dramatic effect on bilayer graphene than monolayer graphene
because the quasi-particles are changed in a fundamental way; the dispersion
goes from a quadratic band touching point to linearly dispersing Dirac cones.
We illustrate that a 1D superlattice of either the chemical potential or an
interlayer bias generates multiple anisotropic Dirac cones. General arguments
delineate how certain symmetries protect the Dirac points. We then map the
Hamiltonian of an interlayer bias superlattice onto a chain model comprised of
"topological" modes. This is followed by another study that considers the
effect of a magnetic field on graphene superlattices. We show that
magnetotransport measurements in a weak perpendicular magnetic field probe the
number of emergent Dirac points and reveal details about the dispersion. In the
case of bilayer graphene, we also discuss the properties of kink states in an
applied magnetic field. Finally, we investigate local moment formation of
adatoms on bilayer graphene using an Anderson impurity model. We identify
regions where the local moments can be turned on or off by applying a external
electric fields. In addition, we compute the RKKY interaction between local
moments and show how it too can be controlled with electric fields.
