  Charge carriers of graphene show neutrino-like linear energy dispersions as
well as chiral behavior near the Dirac point. Here we report highly unusual and
unexpected behaviors of these carriers in applied external periodic potentials,
i.e., in graphene superlattices. The group velocity renormalizes highly
anisotropically even to a degree that it is not changed at all for states with
wavevector in one direction but is reduced to zero in another, implying the
possibility that one can make nanoscale electronic circuits out of graphene not
by cutting it but by drawing on it in a non-destructive way. Also, the type of
charge carrier species (e.g. electron, hole or open orbit) and their density of
states vary drastically with the Fermi energy, enabling one to tune the Fermi
surface-dominant properties significantly with gate voltage. These results
address the fundamental question of how chiral massless Dirac fermions
propagate in periodic potentials and point to a new possible path for nanoscale
electronics.
