Low-energy approximation in the theory of adsorption on graphene

Physics of the Solid State - The effect of the linear approximation of the electronic spectrum of single-layer graphene (low-energy approximation) on the magnitude of charge transfer between an...     

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.     

Low-energy limit of chiral meson theory

Based on a phenomenologically successful effective chiral theory of pseudoscalar, vector, and axial-vector mesons, all the coefficients of the chiral perturbation theory are predicted. There is no new adjustable parameter in these predictions. Up to O(m ² _q) the formulas of the masses of the pseudoscalar mesons are the same as the ones obtained by ChPT. Received: 31 August 2000 / Accepted: 16 March 2001     

The ground state of graphene and graphene disordered by vacancies

Graphene clusters consisting of 24–150 carbon atoms and hydrogen termination at the zigzag boundary edges have been studied, as well as clusters disordered by vacancy(s). Density Function Theory and Gaussian03 software were used to calculate graphene relative stability, desorption energy, band gap, density of states, surface shape, dipole momentum and electrical polarization of all clusters by applying the hybrid exchange-correlation functional Beke–Lee–Yang–Parr. Furthermore, infrared frequencies were calculated for two of them. Different basis sets, 6–31g**, 6–31g* and 6–31g, depending on the sizes of clusters are considered to compromise the effect of this selection on the calculated results. We found that relative stability and the gap decreases according to the size increase of the graphene cluster. Mulliken charge variation increases with the size. For about 500 carbon atoms, a zero HOMO–LUMO gap amount is predicted. Vacancy generally reduces the stability and having vacancy affects the stability differently according to the location of vacancies. Surface geometry of each cluster depends on the number of vacancies and their locations. The energy gap changes as with the location of vacancies in each cluster. The dipole momentum is dependent on the location of vacancies with respect to one another. The carbon–carbon length changes according to each covalence band distance from the boundary and vacancies. Two basis sets, 6-31g* and 6-31g**, predict equal amount for energy, gap and surface structure, but charge distribution results are completely different.     

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 .     

Conductivity of disordered graphene at half filling

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder at half filling. We show that the transport properties of the system depend strongly on the symmetry of disorder. We find that the localization is ineffective if the randomness preserves one of the chiral symmetries of the clean Hamiltonian or does not mix valleys. We obtain the exact value of minimal conductivity 4e²/πh in the case of chiral disorder. For long-range disorder (decoupled valleys), we derive the effective field theory. In the case of smooth random potential, it is a symplectic-class sigma-model including a topological term with θ=π. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e²/h. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and the conductivity acquires the value characteristic for the quantum Hall transition.     

Suppression of magnetotransport in strongly disordered graphene

A tight-binding model with randomly fluctuating atomic positions is studied to discuss the effect of strong disorder in graphene. We employ a strong-disorder expansion for the transport quantities and find a diffusive behavior, where the conductivity is decreasing with increasing disorder. For sufficiently strong disorder the magnetic field drops out of the diffusion coefficient and the conductivity. This signals a strong suppression of magnetotransport effects, a result which is consistent with recent experimental observations by Morozov et al.     

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.     

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)].     

Low-energy termination of graphene edges via the formation of narrow nanotubes

We demonstrate that free graphene sheet edges can curl back on themselves, reconstructing as nanotubes. This results in lower formation energies than any other nonfunctionalized edge structure reported to date in the literature. We determine the critical tube size and formation barrier and compare with density functional simulations of other edge terminations including a new reconstructed Klein edge. Simulated high resolution electron microscopy images show why such rolled edges may be difficult to detect. Rolled zigzag edges serve as metallic conduction channels, separated from the neighboring bulk graphene by a chain of insulating sp(3)-carbon atoms, and introduce van Hove singularities into the graphene density of states.     

Edge states versus diffusion in disordered graphene flakes

We study the localization properties of the wavefunctions in graphene flakes with short range disorder, via the numerical calculation of the inverse participation ratio (IPR) and its scaling which provides the fractal dimension D ₂. We show that the edge states which exist at the Dirac point of ballistic graphene (no disorder) with zig-zag edges survive in the presence of weak disorder with wavefunctions localized at the boundaries of the flakes. We argue, that there is a strong interplay between the underlying destructive interference mechanism of the honeycomb lattice of graphene leading to edge states and the diffusive interference mechanism introduced by the short-range disorder. This interplay results in a highly abnormal behavior, wavefunctions are becoming progressively less localized as the disorder is increased, indicated by the decrease of the average ?IPR? and the increase of D ₂. We verify, that this abnormal behavior is absent for graphene flakes with armchair edges which do not provide edge states.     

Numerical study of localization length in disordered graphene nanoribbons

In this work, we study quantum transport properties of a defective graphene nanoribbon (DGNR) attached to two semi-infinite metallic armchair graphene nanoribbon (AGNR) leads. A line of defects is considered in the GNR device with different configurations, which affects on the energy spectrum of the system. The calculations are based on the tight-binding model and Green’s function method, in which localization length of the system is investigated, numerically. By controlling disorder concentration, the extended states can be separated from the localized states in the system. Our results may have important applications for building blocks in the nano-electronic devices based on GNRs.     

Self-consistent cluster theory of disordered alloys

The coherent potential approximation is not sufficiently accurate to describe the details of the energy spectrum of a disordered alloy when the mean free path is short. A new approximation based on treating, self-consistently, clusters of sites is introduced.     

The supersymmetric theory of disordered heteropolymers

The effective equation of motion for describing the alternation of monomers of different sorts along a heteropolymer chain is proposed. This equation is used for constructing a self-consistent supersymmetric scheme that makes it possible to derive equations for the structure factor and the Green function. The effects of memory and ergodicity loss are studied as functions of the temperature and the intensity of the frozen disorder in the alternation of monomers. The phase diagram that determines the existence domains of nonergodic and frozen states is constructed.     

Quantum transport in disordered graphene: A theoretical perspective

The present theoretical review puts into perspective simulations of quantum transport properties in disordered graphene-based materials. In particular, specific effects induced by short versus long range scattering on the minimum conductivity, weak (anti-)localization, and strongly insulating regimes are discussed in depth. Using various types of disorder profiles (random fluctuations of the local impurity potential, long range Coulomb scatterers or more intrusive chemical functionalizations), universal aspects of transport as well as novel features in chemically modified graphene-based materials are depicted, especially in the cases of oxygen and hydrogen atoms adsorption. Finally, our theoretical results are compared to experimental measurements.     

Bogoliubov theory on the disordered lattice

Quantum fluctuations of Bose-Einstein condensates trapped in disordered lattices are studied by inhomogeneous Bogoliubov theory. Weak-disorder perturbation theory is applied to compute the elastic scattering rate as well as the renormalized speed of sound in lattices of arbitrary dimensionality. Furthermore, analytical results for the condensate depletion are presented, which are in good agreement with numerical data.     

Phonon thermal conductance of disordered graphene strips with armchair edges

Based on the model of lattice dynamics together with the transfer matrix technique, we investigate the thermal conductances of phonons in quasi-one-dimensional disordered graphene strips with armchair edges using Landauer formalism for thermal transport. It is found that the contributions to thermal conductance from the phonon transport near von Hove singularities is significantly suppressed by the presence of disorder, on the contrary to the effect of disorder on phonon modes in other frequency regions. Besides the magnitude, for different widths of the strips, the thermal conductance also shows different temperature dependence. At low temperatures, the thermal conductance displays quantized features of both pure and disordered graphene strips implying that the transmission of phonon modes at low frequencies are almost unaffected by the disorder.