Ana L. C. Pereira

Inner and outer edge states in graphene rings: A numerical investigation

We numerically investigate quantum rings in graphene and find that their electronic properties may be strongly influenced by the geometry, the edge symmetries, and the structure of the corners. Energy spectra are calculated for different geometries (triangular, hexagonal, and rhombus-shaped graphene rings) and edge terminations (zigzag, armchair, as well as the disordered edge of a round geometry). The states localized at the inner edges of the graphene rings describe different evolution as a function of magnetic field when compared to those localized at the outer edges. We show that these different evolutions are the reason for the formation of subbands of edge-states energy levels, separated by gaps (anticrossings). It is evident from mapping the charge densities that the anticrossings occur due to the coupling between inner and outer edge states.

Third edge for a graphene nanoribbon: A tight-binding model calculation

The electronic and transport properties of an extended linear defect embedded in a zigzag nanoribbon of realistic width are studied, within a tight binding model approach. Our results suggest that such defect profoundly modify the properties of the nanoribbon, introducing new conductance quantization values and modifying the conductance quantization thresholds. The linear defect along the nanoribbon behaves as an effective third edge of the system, which shows a metallic behavior, giving rise to new conduction pathways that could be used in nanoscale circuitry as a quantum wire.

Tunable resonances due to vacancies in graphene nanoribbons

The coherent electron transport along zigzag and metallic armchair graphene nanoribbons in the presence of one or two vacancies is investigated. Having in mind atomic scale tunability of the conductance fingerprints, the primary focus is on the effect of the distance to the edges and inter vacancies spacing. An involved interplay of vacancies sublattice location and nanoribbon edge termination, together with the spacing parameters lead to a wide conductance resonance line shape modification. Turning on a magnetic field introduces a new length scale that unveils counter-intuitive aspects of the interplay between purely geometric aspects of the system and the underlying atomic scale nature of graphene.

Valley polarization effects on localization in graphene Landau levels

Effects of disorder and valley polarization in graphene are investigated in the quantum Hall regime. We find anomalous localization properties for the lowest Landau level (LL), where disorder can induce wavefunction delocalization (instead of localization), both for white-noise and gaussian-correlated disorder. We quantitatively identify the contribution of each sublattice to wavefunction amplitudes. Following the valley (sublattice) polarization of states within LLs for increasing disorder we show: (i) valley mixing in the lowest LL is the main effect behind the observed anomalous localization properties, (ii) the polarization suppression with increasing disorder depends on the localization for the white-noise model, while, (iii) the disorder induces a partial polarization in the higher Landau levels for both disorder models.

Splitting of critical energies in the n=0 Landau level of graphene

The lifting of the degeneracy of states from the graphene n=0 Landau level (LL) is investigated through a non-interacting tight-binding model with random hoppings. A disorder-driven splitting of two bands and of two critical energies is observed by means of density of states and participation ratio calculations. The analysis of the probability densities of the states within the n=0 LL provides some insights into the interplay of lattice and disorder effects on the splitting process. An uneven spatial distribution of the wavefunction amplitudes between the two graphene sublattices is found for the states in between the two split peaks. It is shown that as the splitting is increased (linear increasing with disorder and square root increasing with magnetic field), the two split levels also get increasingly broadened, in such a way that the proportion of overlapped states remains approximately constant for a wide range of disorder or magnetic field variation.

Quantifying the levitation picture of extended states in lattice models

The behavior of extended states is quantitatively analyzed for two-dimensional lattice models. A levitation picture is established for both white-noise and correlated disorder potentials. In a continuum limit window of the lattice models we find simple quantitative expressions for the extended states levitation, suggesting an underlying universal behavior. On the other hand, these results point out that the quantum Hall phase diagrams may be disorder dependent.

Extended state floating up in a lattice model: bona fide levitation fingerprints, irrespective of the correlation length

Abstract The evolution of extended states with magnetic field and disorder intensities is investigated for 2D lattice models. The floating-up picture is revealed when the shift of the extended state, relative to the density of states, is properly taken into account, either for white-noise or correlated disorder.

Hidden scaling in the quantum Hall metal-insulator transition

Scaling properties of the quantum Hall metal-insulator transition are severely affected by finite-size effects in small systems. Surprisingly, despite the narrow spatial range where probability structure functions exhibitmultifractal scaling, we clearly verify the existence of extended self-similarity-a hidden infrared scaling phenomenon related to the peculiar form of the crossover at the onset of nonmultifractal behavior. As finite-size effects get stronger for structure functions with negative orders, the parabolic approximation for the multifractal spectrum loses accuracy. However, by means of an extended self-similarity analysis, an improved evaluation of the multifractal exponents is attained for negative orders too, rendering them consistent with previous results, which rely on computations performed for considerably larger systems.

GRAPHENE IN THE QUANTUM HALL REGIME: EFFECTS OF VACANCIES, SUBLATTICE POLARIZATION AND DISORDER

We investigate the effects of vacancies, disorder and sublattice polarization on the electronic properties of a monolayer graphene in the quantum Hall regime. Energy spectra as a function of magnetic field and the localization properties of the states within the graphene Landau levels (LLs) are calculated through a tight-binding model. We first discuss our results considering vacancies in the lattice, where we show that vacancies introduce extra levels (or well-defined bands) between consecutive LLs. An striking consequence here is that extra Hall resistance plateaus are expected to emerge when an organized vacancy superlattice is considered. Secondly, we discuss the anomalous localization properties we have found for the lowest LL, where an increasing disorder is shown to enhance the wave functions delocalization (instead of inducing localization). This unexpected effect is shown to be directly related to the way disorder increasingly destroys the sublattice (valley) polarization of the states in the lowest LL. The reason why this anomalous disorder effect occurs only for the zero-energy LL is that, in absence of disorder, only for this level all the states are sublattice polarized, i.e., their wave functions have amplitudes in only one of the sublattices.