  We demonstrate the existence of localized states in close vicinity of a
linear defect in graphene. These states have insulating or conducting
character. Insulating states form a flat band, while conducting states present
a slowdown of the group velocity which is not originated by many-body
interactions and it is controlled by the interface properties. For appropriate
boundary conditions, the conducting states exhibit momentum-valley locking and
protection from backscattering effects. These findings provide a contribution
to the recent discussion on the origin of correlated phases in graphene.
