Abstract:Bilayer graphene is an interesting candidate for a semiconductor with an electric field tunable bandgap. We show that a sign reversal of the electric field leads to topologically confined one dimensional modes akin to domain wall fermions. These kink modes get converted into a tunable 2-band Luttinger liquid in the presence of interactions, with observable consequences for tunneling and transport. We argue that the observed hopping conduction in transport may arise from such kink states generated by impurities. We also study periodic potential variation, i.e. superlattices, in monolayer and bilayer graphene, finding new Dirac fermion modes in the dispersion which can be revealed by magnetotransport studies. In monolayer graphene, we find that a moderate magnetic field leads to a reversal of the transport anisotropy imposed by the superlattice due to the dispersion of the zeroth Landau level, an effect which may find switch-type applications.
