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

Abstract

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.

Recovery of the scattering symmetry looking at the conductance in asymmetric graphene nano-ribbons systems using pseudo-spin filters

“…On the other hand, when we move away from the Dirac point (right panel of figure 1(b)) the first signs of backscattering are observed. This can be inferred, as reported in previous works, by the splitting of the conductance and the freezing of the partial pseudo-spin polarization [16,17] (in the present case the partial pseudo-spin polarization is only polarized using sites B). We can improve the definition of the conductance's splitting by increasing L. Furthermore, if we consider n filters in the system we will observe n splittings in the conductance (not shown here).…”

“…As shown in previous works [15][16][17], the effects produced by the pseudo-spin filters are related to the hyperboloid subbands inside the applied barrier region, figure 1. We notice from figure 1(a) that as we increase V (the potential barrier energy) the lower hyperboloid sub-bands are shifted towards the Dirac point (E = 0).…”

“…In figures 1(b) and (c) we present the most noticeable characteristics of the effects produced by the pseudo-spin filters in systems with multiple filters. In figure 1(b), as shown in previous works, the conductance as a function of the applied voltage shows that the width of the conductance oscillation decreases as we increase V since more hyperboloid sub-bands begin to contribute inside the barrier region [17]. This effect is related to the quirality loss between the hole-type wave-function (inside the barrier) and the electron-type wave-function (outside the barrier).…”

“…An inverse relation between the conductance and the pseudo-spin polarization (at each side of the barriers) was previously reported using pseudo-spin filters [17] (i.e. barriers with hyperboloid sub-bands contributions).…”

“…In previous works [15][16][17] it was shown the existence of polarized pseudo-spin currents at each side of an applied barrier in armchair ribbon systems, and also at each side of a sequence of quantum dots [16]. These effects were attributed to a local decrease of the quasi-particles' quirality (within the barrier region) induced by the participation of the appliedbarrier's hyperboloid sub-bands that arise with high voltages [17]. No technological applications were given in those works for the studied systems, however they can be used to manipulate pseudo-spin currents through the graphene nano-ribbon.…”