  Conductance fluctuations produced by the presence of disorder in zigzag and
armchair graphene nanoribbons are studied. We show that quantum transport in
zigzag nanoribbons takes place via edge states which are exponentially
localized, as in the standard Anderson localization problem, whereas for
armchair nanoribbons the symmetry of the graphene sublattices produces
anomalous localization, or delocalization. We show that these two different
electron localizations lead to significant differences of the conductance
statistics between zigzag and armchair nanoribbons. In particular, armchair
nanoribbons show nonconventional large conductance fluctuations relative to
those of Anderson-localized electrons. We calculate analytically the complete
distribution of conductances for both types of ribbons. Without free fitting
parameters, we verify our theoretical results by performing numerical
simulations of disordered zigzag and armchair nanoribbons of experimentally
achievable lengths and widths.
