Abstract:Motivated by the recently observed sublattice asymmetry of substitutional nitrogen impurities in CVD grown graphene, we show, in a mathematically transparent manner, that oscillations in the local density of states driven by the presence of substitutional impurities are responsible for breaking the sublattice symmetry. While these oscillations are normally averaged out in the case of randomly dispersed impurities, in graphene they have either the same, or very nearly the same, periodicity as the lattice. As a … Show more
“…In general, this occurs if the impurities are randomly located in sites corresponding to the sub-lattice LS and therefore they do not contribute to the electronic transport. Thus, the recent reported phenomenon [23][24][25][26] in which doping occurs asymmetrically between the two sublattices (A and B) is a current interesting topic related to our work.…”
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 sublattices 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.
“…In general, this occurs if the impurities are randomly located in sites corresponding to the sub-lattice LS and therefore they do not contribute to the electronic transport. Thus, the recent reported phenomenon [23][24][25][26] in which doping occurs asymmetrically between the two sublattices (A and B) is a current interesting topic related to our work.…”
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 sublattices 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.
“…35 These self-organized structures of the nitrogen doped graphene are stabilized by the impurity-impurity interaction that favors impurities on the same sublattice, an effect that scales quickly with the impurity concentration. 36 For the case of diluted fluorine adatoms on BLG there are no evidences of clustering on one sublattice. Moreover, the interaction between impurities on graphene is known to depend crucially on the type of impurity and on the adsorption geometry.…”
Section: Numerical Results For the Many Impurities Casementioning
We analyze the electronic properties of bilayer graphene with Bernal stacking and a low concentration of adatoms. Assuming that the host bilayer lies on top of a substrate, we consider the case where impurities are adsorbed only on the upper layer. We describe non-magnetic impurities as a single orbital hybridized with carbon's p z states. The effect of impurity doping on the local density of states with and without a gated electric field perpendicular to the layers is analyzed. We look for Anderson localization in the different regimes and estimate the localization length. In the biased system, the field induced gap is partially filled by strongly localized impurity states. Interestingly, the structure, distribution and localization length of these states depend on the field polarization.
“…Large domains are found with N atoms primarily occupying a single sublattice [8][9][10][11][12]. This behavior depends on growth conditions, and theoretical works suggest possible mechanisms including preferential impurity positioning relative to the edges during growth [13] and interimpurity interactions in disordered ensembles [14,15]. Subsequent studies of N-doped graphene treated by hightemperature annealing [16], and of graphene decorated by hydrogen adatoms [17], suggest that asymmetric distributions may also arise in other scenarios.…”
Recent experimental findings and theoretical predictions suggest that nitrogen-doped CVD-grown graphene may give rise to electronic band gaps due to impurity distributions which favour segregation on a single sublattice. Here we demonstrate theoretically that such distributions lead to more complex behaviour in the presence of edges, where geometry determines whether electrons in the sample view the impurities as a gap-opening average potential or as scatterers. Zigzag edges give rise to the latter case, and remove the electronic bandgaps predicted in extended graphene samples. We predict that such behaviour will give rise to leakage near grain boundaries with a similar geometry or in zigzag-edged etched devices. Furthermore, we examine the formation of one-dimensional metallic channels at interfaces between different sublattice domains, which should be observable experimentally and offer intriguing waveguiding possibilities.
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