Edge states of graphene bilayer strip

The electronic structure of the zig-zag bilayer strip is analyzed. The electronic spectraof the bilayer strip is computed. The dependence of the edge state band flatness on thebilayer width is found. The density of states at the Fermi level is analytically computed.It is shown that it has the singularity which depends on the width of the bilayer strip.There is also asymmetry in the density of states below and above the Fermi energy.     

Weak localization in graphene flakes

We show that the manifestation of quantum interference in graphene is very different from that in conventional two-dimensional systems. Because of the chiral nature of charge carriers, it is not only sensitive to inelastic, phase-breaking scattering, but also to a number of elastic scattering processes. We study weak localization in different samples and at different carrier densities, including the Dirac region, and find the characteristic rates that determine it. We show how the shape and quality of graphene flakes affect the values of the elastic and inelastic rates and discuss their physical origin.     

Edge states and distributions of edge currents in semi-infinite graphene

The distributions of edge currents in semi-infinite graphene under a uniform perpendicular magnetic field are investigated. We show unambiguously that the edge current is finite at the armchair edge but vanishes at the zigzag edge. It is shown that the current density oscillates with the distance away from the boundary and tends to zero deep inside the graphene. The study shows that the total current is independent of edge configurations. The interplay of the bulk and edge contributions to the total current is presented. The quantized plateaus of Hall conductivity at (4e ²/h)(n+1/2) provide a direct evidence of the connection between the edge states and topological properties of relativistic fermions in a magnetic field.     

Edge effects on the characteristics of uranium diffusion on graphene and graphene nanoribbons

The first principles density-functional theoretical calculations of U adatom adsorption and diffusion on a planar graphene and quasi-one-dimensional graphene nanoribbons(GNRs) are performed. An energetic preference is found for U adatom diffusing to the hollow sites of both graphene and GNRs surface. A number of U distinctive diffusion paths either perpendicular or parallel to the ribbon growth direction are examined. The edge effects are evidenced by the calculated energy barriers of U adatom diffusion on armchair and zigzag nanoribbons surfaces. The calculation results indicate that the diffusion of U adatom from the inner site toward the edge site is a feasible process, particularly in zigzagGNR. It is viable to control the initial morphology of nuclear carbon material to retard the diffusion and concentration of nuclides.     

Edge states at the interface between monolayer and bilayer graphene

The electronic properties for monolayer-bilayer hybrid graphene with zigzag interface are studied by both the Dirac equation and numerical calculation in zero field and in a magnetic field. Basically there are two types of zigzag interface dependent on the way of lattice stacking at the edge. Our study shows they have different locations of the localized edge states. Accordingly, the energy-momentum dispersion and local density of states behave quit differently along the interface near the Fermi energy EF=0.     

Electronic shell and supershell structure in graphene flakes

We use a simple tight-binding (TB) model to study electronic properties of free graphene flakes. Valence electrons of triangular graphene flakes show a shell and supershell structure which follows an analytical expression derived from the solution of the wave equation for triangular cavity. However, the solution has different selection rules for triangles with armchair and zigzag edges, and roughly 40?000 atoms are needed to see clearly the first supershell oscillation. In the case of spherical flakes, the edge states of the zigzag regions dominate the shell structure which is thus sensitive to the flake diameter and center. A potential well that is made with external gates cannot have true bound states in graphene due to the zero energy band gap. However, it can cause strong resonances in the conduction band.     

Critical wavefunctions in disordered graphene

In order to elucidate the presence of non-localized states in doped graphene, a scaling analysis of the wavefunction moments, known as inverse participation ratios, is performed. The model used is a tight-binding Hamiltonian considering nearest and next-nearest neighbors with random substitutional impurities. Our findings indicate the presence of non-normalizable wavefunctions that follow a critical (power-law) decay, which show a behavior intermediate between those of metals and insulators. The power-law exponent distribution is robust against the inclusion of next-nearest neighbors and growing the system size.     

Spin relaxation times in disordered graphene

We consider two mechanisms of spin relaxation in disordered graphene. i) Spin relaxation due to curvature spin orbit coupling caused by ripples. ii) Spin relaxation due to the interaction of the electronic spin with localized magnetic moments at the edges. We obtain analytical expressions for the spin relaxation times τ_SO and τ_J due to both mechanisms and estimate their values for realistic parameters of graphene samples. We obtain that spin relaxation originating from these mechanisms is very weak and spin coherence is expected in disordered graphene up to samples of length .     

Off-perturbative states in disordered systems

The systematic approach for the off-perturbative calculations in disordered systems is developed. The proposed scheme is applied for the random temperature and the random field ferromagnetic Ising models. It is shown that away from the critical point, in the paramagnetic phase of the random temperature model, and in the ferromagnetic phase of the random field one, the free energy contains non-analytic contributions which have the form of essential singularities. It is demonstrated that these contributions appear due to localized in space instanton-like excitations.     

Quasiparticle states in disordered superfluids

A model for disordered superfluids and superconductors is considered in terms of the Bogoliubov-de Gennes equation with a random order parameter field. Two characteristic cases are distinguished: model I with a real order parameter (time reversal invariant system) and model II with a complex order parameter (broken time reversal invariance). The fluctuations of the order parameter close the gap in both models, and we investigate the states at the center of the filled gap. The two models have distinctive properties in terms of the quasiparticle states due to different symmetries. Model II exhibits only localized quasiparticle states at the band center. In contrast, the fluctuations of the real order parameter of model I can be described by a nonlinear sigma model which leads to a transition from localized to extended states for dimensionsd>2.     

Low-energy theory of disordered graphene

At low values of external doping, graphene displays a wealth of unconventional transport properties. Perhaps most strikingly, it supports a robust "metallic" regime, with universal conductance of the order of the conductance quantum. We here apply a combination of mean-field and bosonization methods to explore the large scale transport properties of the system. We find that, irrespective of the doping level, disordered graphene is subject to the common mechanisms of Anderson localization. However, at low doping a number of renormalization mechanisms conspire to protect the conductivity of the system, to an extend that strong localization may not be seen even at temperatures much smaller than those underlying present experimental work.     

Atomistic simulations of the sliding friction of graphene flakes

Using a tight-binding atomistic simulation, we simulate the recent atomic-force microscopy experiments probing the slipperiness of graphene flakes made slide against a graphite surface. Compared to previous theoretical models, where the flake was assumed to be geometrically perfect and rigid, while the substrate is represented by a static periodic potential, our fully-atomistic model includes quantum mechanics with the chemistry of bond breaking and bond formation, and the flexibility of the flake. These realistic features, include in particular the crucial role of the flake rotation in determining the static friction, in qualitative agreement with experimental observations.     

Electronic heat capacity in disordered graphene systems

We analyzed the electronic heat capacity of graphene systems in the presence of disorder. We consider the case of strong scatterers, working in the unitary limit. The temperature dependence of the electronic heat capacity is analyzed. Close to the clean limit we obtained the quadratic temperature dependence, corrected with a temperature and disorder dependent factor which slightly enhance the heat capacity. At very low temperatures, and in the presence of disorder, we obtained a linear temperature dependence of the electronic heat capacity. We also analyzed the temperature dependence of the electronic heat capacity in the case of extrinsic graphene.     

Abnormal electronic transport in disordered graphene nanoribbon

We investigate the conductivity σ of graphene nanoribbons with zigzag edges as a function of Fermi energy E_F in the presence of the impurities with different potential range. The dependence of σ(E_F) displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of σ(E_F) and a wide dip near the Dirac point, due to the special properties of long range potential and edge states. These behaviors agree well with the results from a recent experiment by Miao et al. [Science 317 (2007) 1530 (SOM)].     

Magnetism in disordered graphene and irradiated graphite

The magnetic properties of disordered graphene and irradiated graphite are systematically studied using a combination of mean-field Hubbard model and first-principles calculations. By considering large-scale disordered models of graphene, I conclude that only single-atom defects can induce ferromagnetism in graphene-based materials. The preserved stacking order of graphene layers is shown to be another necessary condition for achieving a finite net magnetic moment of irradiated graphite. Ab initio calculations of hydrogen binding and diffusion and of interstitial-vacancy recombination further confirm the crucial role of stacking order in pi-electron ferromagnetism of proton-bombarded graphite.     

Chirality effect in disordered graphene ribbon junctions

We investigate the influence of edge chirality on the electronic transport in clean or disordered graphene ribbon junctions. By using the tight-binding model and the Landauer-Büttiker formalism, the junction conductance is obtained. In the clean sample, the zero-magnetic-field junction conductance is strongly chirality-dependent in both unipolar and bipolar ribbons, whereas the high-magnetic-field conductance is either chirality-independent in the unipolar or chirality-dependent in the bipolar ribbon. Furthermore, we study the disordered sample in the presence of magnetic field and find that the junction conductance is always chirality-insensitive for both unipolar and bipolar ribbons with adequate disorders. In addition, the disorder-induced conductance plateaus can exist in all chiral bipolar ribbons provided the disorder strength is moderate. These results suggest that we can neglect the effect of edge chirality in fabricating electronic devices based on the magnetotransport in a disordered graphene ribbon.