  The conductance of metallic graphene nanoribbons (GNRs) with single defects
and weak disorder at their edges is investigated in a tight-binding model. We
find that a single edge defect will induce quasi-localized states and
consequently cause zero-conductance dips. The center energies and breadths of
such dips are strongly dependent on the geometry of GNRs. Armchair GNRs are
much more sensitive to a vacancy than zigzag GNRs, but are less sensitive to a
weak scatter. More importantly, we find that with a weak disorder, zigzag GNRs
will change from metallic to semiconducting due to Anderson localization. But a
weak disorder only slightly affects the conductance of armchair GNRs. The
influence of edge defects on the conductance will decrease when the widths of
GNRs increase.
