  Graphene revealed a number of unique properties beneficial for electronics.
However, graphene does not have an energy band-gap, which presents a serious
hurdle for its applications in digital logic gates. The efforts to induce a
band-gap in graphene via quantum confinement or surface functionalization have
not resulted in a breakthrough. Here we show that the negative differential
resistance experimentally observed in graphene field-effect transistors of
"conventional" design allows for construction of viable non-Boolean
computational architectures with the gap-less graphene. The negative
differential resistance - observed under certain biasing schemes - is an
intrinsic property of graphene resulting from its symmetric band structure. Our
atomistic modeling shows that the negative differential resistance appears not
only in the drift-diffusion regime but also in the ballistic regime at the
nanometer-scale - although the physics changes. The obtained results present a
conceptual change in graphene research and indicate an alternative route for
graphene's applications in information processing.
