  We study transport properties of graphene with anisotropically distributed
on-site impurities (adatoms) that are randomly placed on every third line drawn
along carbon bonds. We show that stripe states characterized by strongly
suppressed back-scattering are formed in this model in the direction of the
lines. The system reveals L\'evy-flight transport in stripe direction such that
the corresponding conductivity increases as the square root of the system
length. Thus, adding this type of disorder to clean graphene near the Dirac
point strongly enhances the conductivity, which is in stark contrast with a
fully random distribution of on-site impurities which leads to Anderson
localization. The effect is demonstrated both by numerical simulations using
the Kwant code and by an analytical theory based on the self-consistent
$T$-matrix approximation.

Disordered Systems and Neural Networks