Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials0

Graphenes conical valence and conduction bands give rise to charge carriers that have neutrino-like linear energy dispersion and exhibit chiral behaviour near the Dirac points where these bands meet. Such characteristics offer exciting opportunities for the occurrence of new phenomena and the development of high performance electronic devices. Making high quality devices from graphene, which typically involves etching it into nanoscale structures, however, has proven challenging. Here we show that a periodic potential applied by suitably patterned modifications or contacts on graphenes surface leads to further unexpected and potentially useful charge carrier behaviour. Owing to their chiral nature, the propagation of charge carriers through such a graphene superlattice is highly anisotropic, and in extreme cases results in group velocities that are reduced to zero in one direction but are unchanged in another. Moreover, we show that the density and type of carrier species (electron, hole or open orbit) in a graphene superlattice are extremely sensitive to the potential applied, and they may further be tuned by varying the Fermi level. As well as addressing fundamental questions about how the chiral massless Dirac fermions of graphene propagate in a periodic potential, our results suggest the possibility of building graphene electronic circuits from appropriately engineered periodic surface patterns, without the need for cutting or etching.