  Superlattices (SLs) in monolayer and bilayer graphene, formed by spatially
periodic potential variations, lead to a modified bandstructure with extra
finite-energy and zero-energy Dirac fermions with tunable anisotropic
velocities. We theoretically show that transport in a weak perpendicular
(orbital) magnetic field allows one to not only probe the number of emergent
Dirac points but also yields further information about their dispersion. or
monolayer graphene, we find that a moderate magnetic field can lead to a strong
reversal of the transport anisotropy imposed by the SL potential, an effect
which arises due to the SL induced dispersion of the zero energy Landau levels.
This effect may find useful applications in switching or other devices. For
bilayer graphene, we discuss the structure of Landau level wave functions and
local density of states in the presence of a uniform bias, as well as in the
presence of a kink in the bias which leads to topologically bound `edge
states'. We consider implications of these results for scanning tunneling
spectroscopy measurements, valley filtering, and impurity induced breakdown of
the quantum Hall effect in bilayer graphene.
