Exclusive sub-lattices for extended and localized states in graphene ribbons: their role in Klein tunneling, disorder and magnetic field effects

We report the existence of two sub-lattices in metallic graphene nanoribbons that present a decoupled behavior. Each sub-lattice, one for extended states (ES) and another exclusively for localized states (LS), is formed by a combination of A and B graphene sites. In the sub-lattice ES all electronic transport phenomena occur, including the Klein tunneling through an external applied potential barrier. In contrast, the sub-lattice LS does not contribute to the transport of quasi-particles and strongly localized states are induced within the potential barrier region. The sub-lattices ES and LS are detected by analyzing Klein states and totally localized states that were systematically perturbed by the contributions of hyperboloid bands generated by the potential barrier. This is performed by gradually increasing the energy of the applied potential. The existence of both sub-lattices are tested by considering disorder and magnetic field effects in the system. The results indicate that both sub-lattices behave as if there are decoupled, even at the presence of an external applied barrier and that they can be coupled by applying an external magnetic field.