Graphene ribbons with a line of impurities: Opening of a gap

A tight-binding model is used to study the role of impurities in a graphene ribbon. The graphene ribbon is made of lines of carbon atoms in an armchair or zigzag shape where the impurities are included in the ribbon substitutionally. The addition of a line of impurities opens up a gap in the energy spectrum. The size of it depends in a nonmonotonic way on the position of the impurity line, and also on the strength of the carbon-impurity interaction.