We calculate the carrier density dependent ground state properties of graphene in the presence of random charged impurities in the substrate taking into account disorder and interaction effects non-perturbatively on an equal footing in a self-consistent theoretical formalism. We provide detailed quantitative results on the dependence of the disorder-induced spatially inhomogeneous two-dimensional carrier density distribution on the external gate bias, the impurity density, and the impurity location. We find that the interplay between disorder and interaction is strong, particularly at lower impurity densities. We show that for the currently available typical graphene samples, inhomogeneity dominates graphene physics at low ($\lesssim 10^{12}$ cm$^{-2}$) carrier density with the density fluctuations becoming larger than the average density.
It is shown that a ``vacuum polarization'' induced by Coulomb potential in graphene leads to a strong suppression of electric charges even for undoped case (no charge carriers). A standard linear response theory is therefore not applicable to describe the screening of charge impurities in graphene. In particular, it overestimates essentially the contributions of charge impurities into the resistivity of graphene.
Inherent symmetries of a system lead to multiple degeneracies of its energy spectra. Introducing individual atomic impurities can locally break these symmetries, which is expected to lift the degenerate degrees of freedom around the impurities. Although central to our understanding of the fundamental properties of solids, the broken-symmetry states induced by individual atomic impurities have so far eluded observation. Here, we report nanoscale probing of the broken-symmetry states in graphene induced by two types of individual atomic impurities, i.e., isolated nitrogen dopants and isolated hy…
We develop a first-principles theory of resonant impurities in graphene and show that a broad range of typical realistic impurities leads to the characteristic sublinear dependence of the conductivity on the carrier concentration. By means of density functional calculations various organic groups as well as ad-atoms like H absorbed to graphene are shown to create midgap states within +-0.03eV around the neutrality point. A low energy tight-binding description is mapped out. Boltzmann transport theory as well as a numerically exact Kubo formula approach yield the conductivity of graphene contam…
We report nanocrystalline carbon impurities coexisting with graphene synthesized via chemical vapor deposition (CVD) on platinum. We observe micron-size island-like impurity layers, which can easily be mistaken for second graphene layers in optical microscopy or secondary electron microscopy (SEM). The island orientation depends on the crystalline orientation of the Pt, as shown by electron backscatter diffraction(EBSD), indicating growth of amorphous carbon below graphene. Dark-field TEM indicates that in addition to uniform single-crystal graphene, our sample is decorated with nanocrystallin…
We theoretically study the atomic structure and energetics of silicon and silicon-nitrogen impurities in graphene. Using density-functional theory, we get insight into the atomic structures of the impurities, evaluate their formation energies and assess their abundance in realistic samples. We find that nitrogen, as well as oxygen and hydrogen, are trapped at silicon impurities, considerably altering the electronic properties of the system. Furthermore, we show that nitrogen doping can induce local magnetic moments resulting in spin-dependent transport properties, even though neither silicon n…
We investigate the conductivity of doped graphene in the semiclassical Boltzmann limit, as well as the conductivity minimum within the self-consistent transport theory. Using the hard-disk model for a two-dimensional distribution of impurities gives rise to both strong increase in the slope of conductivity at low charge carrier densities in graphene and a strongly sub-linear behavior of the conductivity at high charge carrier densities when the correlation distance between the impurities is large. On the other hand, we find that a super-linear dependence of the conductivity on charge carrier d…
In graphene devices with a varying degree of disorders as characterized by their carrier mobility and minimum conductivity, we have studied the thermoelectric power along with the electrical conductivity over a wide range of temperatures. We have found that the Mott relation fails in the vicinity of the Dirac point in high-mobility graphene. By properly taking account of the high temperature effects, we have obtained good agreement between the Boltzmann transport theory and our experimental data. In low-mobility graphene where the charged impurities induce relatively high residual carrier dens…
We point out the existence of finite charge and spin Hall conductivities of graphene in the presence of a spin orbit interaction (SOI) and localized magnetic impurities. The SOI in graphene results in different transverse forces on the two spin channels yielding the spin Hall current. The magnetic scatterers act as spin-dependent barriers, and in combination with the SOI effect lead to a charge imbalance at the boundaries. As indicated here, the charge and spin Hall effects should be observable in graphene by changing the chemical potential close to the gap.
Resonant scattering of electrons with low energies (as compared to the bandwidth) on a single neutral short-range impurity in graphene is analyzed theoretically, taking into account the valley degeneracy. Resonances dramatically increase the scattering cross-section and introduce a strong energy dependence. Analysis of the tight-binding model shows that resonant scattering is typical for generic impurities as long as they are sufficiently strong (the potential is of the order of the electron bandwidth or higher).
The ground-state and the transport properties of graphene subject to the potential of in-plane charged impurities are studied. The screening of the impurity potential is shown to be nonlinear, producing a fractal structure of electron and hole puddles. Statistical properties of this density distribution as well as the charge compressibility of the system are calculated in the leading-log approximation. The conductivity depends logarithmically on $α$, the dimensionless strength of the Coulomb interaction. The theory is asymptotically exact when $α$ is small, which is the case for graphene on a …
Screening of charge impurities in graphene is analyzed using the exact solution for vacuum polarization obtained from the massless Dirac-Kepler problem. For the impurity charge below certain critical value no density perturbation is found away from the impurity, in agreement with the linear response theory result. For supercritical charge, however, the polarization distribution is shown to have a power law profile, leading to screening of the excess charge at large distances. The Dirac-Kepler scattering states give rise to standing wave oscillations in the local density of states which appear …
We study the problem of Coulomb field-induced charging of the ground state in a system of 2D massive Dirac particles (gapped graphene). As in its 3D QED counterpart, the critical Coulomb coupling is renormalized to higher values, compared to the massless case. We find that in gapped graphene a novel supercritical regime is possible, where the screening charge is comparable to the impurity charge, thus leading to suppression of the Coulomb field at nanometer scales. We corroborate this with numerical solution of the tight-binding problem in the honeycomb lattice.
We experimentally study the effect of different scattering potentials on the flicker noise observed in graphene devices on silica substrates. The noise in nominally identical devices is seen to behave in two distinct ways as a function of carrier concentration, changing either monotonically or nonmonotonically. We attribute this to the interplay between long- and short-range scattering mechanisms. Water is found to significantly enhance the noise magnitude and change the type of the noise behaviour. By using a simple model, we show that water is a source of long-range scattering.
While imaging individual atoms can routinely be achieved in high resolution transmission electron microscopy, visualizing the potential distribution of individually charged adsorbates leading to a phase shift of the probing electron wave is still a challenging task. Low-energy electrons (30 - 250 eV) are sensitive to localized potential gradients. We employed low-energy electron holography to acquire in-line holograms of individual charged impurities on free-standing graphene. By applying an iterative phase retrieval reconstruction routine we recover the potential distribution of the localized…
Interaction between adsorbed atoms in graphene is studied using a combination of DFT and the path integral formalism. Our results reveal a complex non-monotonic interaction profile. We show that the strength and sign of the interaction are dictated by the arrangement of impurities, as well as the system doping. These findings can be used to interpret the complex behavior of impurities in experimentally realized systems, as well as other classes of impurities, such as C substitutions in graphene.
Monovalent impurities on graphene can be divided into ionically and covalently bond impurities. The covalent impurities cause universal midgap states as the carbon atom next to the impurity is effectively decoupled from the graphene pi-bands. The electronic structure of graphene suppresses migration of these impurities and making the universal midgap very stable. This effect is strongest for neutral covalently bond impurities. The ionically bond impurities have migration barriers of typically less than 0.1eV. An asymmetry between anions and cations regarding their adsorption sites and topology…
Bound electron states in impure graphene are considered. Short-range perturbations for defect and impurities of the types "local chemical potential" and "local gap" are taken into account.
Experimentally produced graphene sheets exhibit a wide range of mobility values. Both extrinsic charged impurities and intrinsic ripples (corrugations) have been suggested to induce long-range disorder in graphene and could be a candidate for the dominant source of disorder. Here, using large-scale molecular dynamics and quantum transport simulations, we find that the hopping disorder and the gauge and scalar potentials induced by the ripples are short-ranged, in strong contrast with predictions by continuous models, and the transport fingerprints of the ripple disorder are very different from…
We study the interaction between two magnetic adatom impurities in graphene using the Anderson model. The two-impurity Anderson Hamiltonian is solved numerically by using the quantum Monte Carlo technique. We find that the inter-impurity spin susceptibility is strongly enhanced at low temperatures, significantly diverging from the well-known Ruderman-Kittel-Kasuya-Yoshida (RKKY) result which decays as $R^{-3}$.
Bound and resonance electronic states in impure graphene are studied. Short-range perturbations for defects and impurities of the types "local chemical potential" and "local gap" are taken into account. Zero gap and non-zero gap kinds of graphene are considered. A qualitative analysis of the electronic spectrum general features and numeric calculations are presented. A dependence of the resonance widths on the gap value, angular momentum values and the perturbation amplitudes is investigated.
A significant advance toward achieving practical applications of graphene as a two-dimensional material in nanoelectronics would be provided by successful synthesis of both n-type and p-type doped graphene. However reliable doping and a thorough understanding of carrier transport in the presence of charged impurities governed by ionized donors or acceptors in the graphene lattice are still lacking. Here we report experimental realization of few-layer nitrogen-doped (N-doped) graphene sheets by chemical vapor deposition of organic molecule 1, 3, 5-triazine on Cu metal catalyst. By reducing the …
The electronic properties of antimonene, single-layer Sb, are attracting great attention. In this paper, spin transport in armchair antimonene nanoribbon (ASbNR) is investigated. Following the tight-binding model, we calculate both the transmission probability and the conductance by means of the non-equilibrium Green's function (NEGF) method. The effects of an external electric field vertical to the ribbon plane are explored. Our results indicate that the spin-flip rate increases with the vertical electric field. Disorder effects on spin transport are addressed by considering the presence of c…
We study the problem of impurities and mid-gap states in a biased graphene bilayer. We show that the properties of the bound states, such as localization lengths and binding energies, can be controlled externally by an electric field effect. Moreover, the band gap is renormalized and impurity bands are created at finite impurity concentrations. Using the coherent potential approximation we calculate the electronic density of states and its dependence on the applied bias voltage.
We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem.
We study the spin relaxation of charge carriers in graphene in the presence of spin-polarized charged impurities by calculating the time evolution of initially polarized state. The spin relaxation time shows completely different energy behaviour for short-ranged and long-ranged spin scatterers and can be used to identify the dominant source of spin scattering. Our results agree well with recent experimental findings and indicate that their spin relaxation is likely caused by long-ranged scatterers.
In this work, the tridiagonal method is used to distinguish between edges modes and area modes to study the edge sites properties effect on edge localized states of semi-infinite zigzag 2D honeycomb graphene sheet. The results show a realistic behavior for the dependance of edge localized states of zigzag graphene on the edge sites properties which explaining the experimental results of measured local density of states at the edge of graphene, while at the same time removing the inconsistence between the semiconductor behavior found in the experimental data for fabricated GNRs and the expected…
Intervalley charged-impurity scattering processes are examined. It is found that the scattering probability is enhanced due to the Coulomb interaction with the impurity by the Sommerfield factor $F_Z\propto ε^{2\sqrt{1-4g^2}-2}$, where $ε$ is the electron energy and $g$ is the dimensionless constant of the Coulomb interaction.
This article summarizes our understanding of the Kondo effect in graphene, primarily from a theoretical perspective. We shall describe different ways to create magnetic moments in graphene, either by adatom deposition or via defects. For dilute moments, the theoretical description is in terms of effective Anderson or Kondo impurity models coupled to graphene's Dirac electrons. We shall discuss in detail the physics of these models, including their quantum phase transitions and the effect of carrier doping, and confront this with existing experimental data. Finally, we point out connections to …
We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, $Z|e|/r$, in graphene. Our analysis is based on the exact electron Green's function, obtained by using the operator method, and leads to results that are exact in the parameter $Zα$, where $α$ is the "fine structure constant" of graphene. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge $Z_{eff}$, determined by the localized induced charge. We …
Scattering problem for electrons in monolayer graphene with short-range perturbations of the types "local chemical potential" and "local gap" has been solved. Zero gap and non-zero gap kinds of graphene are considered. The determined S-matrix can be used for calculation of such observables as conductance and optical absorption.
The effective spin exchange coupling between impurities (adatoms) on graphene mediated by conduction electrons is studied as a function of the strength of the potential part of the on-site energy $U$ of the electron-adatom interaction. With increasing $U$, the exchange coupling becomes long-range, determined largely by the impurity levels with energies close to the Dirac points. When adatoms reside on opposite sublattices, their exchange coupling, normally antiferromagnetic, becomes ferromagnetic and resonantly enhanced at a specific distance where an impurity level crosses the Dirac point.
We present a theoretical study using density functional calculations of the structural, electronic and magnetic properties of 3d transition metal, noble metal and Zn atoms interacting with carbon monovacancies in graphene. We pay special attention to the electronic and magnetic properties of these substitutional impurities and found that they can be fully understood using a simple model based on the hybridization between the states of the metal atom, particularly the d shell, and the defect levels associated with an unreconstructed D3h carbon vacancy. We identify three different regimes associ…
Spectral and transport properties of doped (or gated) graphene with long range charged impurities are discussed within the self-consistent Born approximation. It is shown how, for impurity concentrations $n_{imp}\gtrsim n$ a finite DOS appears at the Dirac point, the one-particle lifetime no longer scales linearly with the Fermi momentum, and the lineshapes in the spectral function become non-lorentzian. These behaviors are different from the results calculated within the Born approximation. We also calculate the optical conductivity from the Kubo formula by using the self-consistently calcula…
We review the physics of charged impurities in the vicinity of graphene. The long-range nature of Coulomb impurities affects both the nature of the ground state density profile as well as graphene's transport properties. We discuss the screening of a single Coulomb impurity and the ensemble averaged density profile of graphene in the presence of many randomly distributed impurities. Finally, we discuss graphene's transport properties due to scattering off charged impurities both at low and high carrier density.
The growing interest in carbon-based spintronics has stimulated a number of recent theoretical studies on the RKKY interaction in graphene, with the aim of determining the most energetically favourable alignments between embedded magnetic moments. The RKKY interaction in undoped graphene decays faster than expected for conventional two-dimensional materials and recent studies suggest that the adsorption configurations favoured by many transition-metal impurities may lead to even shorter ranged decays and possible sign-changing oscillations. Here we show that these features emerge in a mathemat…
A dilute distribution of magnetic impurities is assumed to be present in doped graphene. We calculate the interaction energy between two magnetic impurities which are coupled via the indirect-exchange or Ruderman-Kittel-Kasuva-Yosida (RKKY) interaction by the doped conduction electrons. The current model is a half-filled $AB$-lattice structure. Our calculations are based on the retarded lattice Green's function formalism in momentum-energy space which is employed in linear response theory to determine the magnetic susceptibility in coordinate space. Analytic results are obtained for gapped gra…
We consider an effect of weak impurities on electronic properties of graphene within the functional renormalization-group approach. The energy dependences of the electronic self-energy and density of states near the neutrality point are discussed. Depending on the symmetry of the impurities, the electronic damping $Γ$ and density of states $ρ$ can deviate substantially from those given by the self-consistent Born approximation. We investigate the crossover from the results of the self-consistent Born approximation, which are valid far from the neutrality point to the strong-coupling (diffusive…
In graphene, charged defects break the electron-hole symmetry and can even give rise to exotic collapse states when the defect charge exceeds a critical value which is proportional to the Fermi velocity. In this work, we investigate the electronic properties of twisted bilayer graphene (tBLG) with charged defects using tight-binding calculations. Like monolayer graphene, tBLG exhibits linear bands near the Fermi level but with a dramatically reduced Fermi velocity near the magic angle (approximately 1.1°). This suggests that the critical value of the defect charge in magic-angle tBLG should al…
We have mapped the Dirac point in exfoliated monolayer and bilayer graphene using spatially resolved scanning tunneling spectroscopy (STS) measurements at low temperature. The Dirac point shifts in energy at different locations in graphene. However, a cross correlation with the topography shows no correlation indicating that topographic features such as ripples are not the primary source of the variation. Rather, we attribute the shift of the Dirac point to random charged impurities located near the graphene. Our findings emphasize the need to advance exfoliated graphene sample preparation to …
The effective interaction between resonant magnetic Anderson impurities in graphene, mediated by conduction electrons, is studied as a function of the strength of the onsite energy level of the impurities and the amplitude of coupling to conduction electrons. The sign and character of the interaction depend on whether the impurities reside on the same or opposite sublattices. For the same (opposite) sublattice, the potential interaction is attractive (repulsive) in the weak coupling limit with $1/R^3$ dependence on the distance; the interaction reverses sign and becomes repulsive (attractive) …
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 pz 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…
We report {\it ab initio} calculations of the structural, electronic and magnetic properties of a graphene monolayer substitutionally doped with Co (Co$_{sub}$) atoms. We focus in Co because among traditional ferromagnetic elements (Fe, Co and Ni), only Co$_{sub}$ atoms induce spin-polarization in graphene. Our results show the complex magnetism of Co substitutional impurites in graphene, which is mapped into simple models such as the $π$-vacancy and Heisenberg model. The links established in our work can be used to bring into contact the engineering of nanostructures with the results of $π$-m…
The effect of electronic interactions in graphene with vacancies or resonant scatterers is investigated. We apply dynamical mean-field theory in combination with quantum Monte Carlo simulations, which allow us to treat non-perturbatively quantum fluctuations beyond Hartree-Fock approximations. The interactions narrow the width of the resonance and induce a Curie magnetic susceptibility, signaling the formation of local moments. The absence of saturation of the susceptibility at low temperatures suggests that the coupling between the local moment and the conduction electrons is ferromagnetic.
We propose that the observed spin-relaxation in bilayer graphene is due to resonant scattering by magnetic impurities. We analyze a resonant scattering model due to adatoms on both dimer and non-dimer sites, finding that only the former give narrow resonances at the charge neutrality point. Opposite to single-layer graphene, the measured spin-relaxation rate in graphene bilayer increases with carrier density. Although it has been commonly argued that a different mechanism must be at play for the two structures, our model explains this behavior rather naturally in terms of different broadening …
We investigate the ballistic electron transport in a monolayer graphene with configurational averaged impurities, located between two clean graphene leads. It is shown that the electron transmission are strongly dependent on the concentration of impurities and the incident energy. In turn, the conductance computed using the Landauer formalism shows a similar behavior to those found in experimental works as a function of the applied voltage for different concentrations of impurities in the limit of low temperatures. In the limit of zero bias voltage, the conductance shows a minimum value which …
In contrast to monolayer graphene, in bilayer graphene (BLG) one can induce a tunable bandgap by applying an external electric field, which makes it suitable for field effect applications. Extrinsic doping of BLGs enriches the electronic properties of the graphene-based family, as their behavior can be switched from an intrinsic small-gap semiconductor to a degenerate semiconductor. In the framework of density functional theory (DFT) calculations, we investigate the electronic and thermoelectric properties of BLGs doped with extrinsic impurities from groups III (B, Al, Ga), IV (Si, Ge) and V (…
This work analyses how impurities and vacancies on the surface of a graphene sample affect its optical conductivity and plasmon excitations. The disorder is analysed in the self-consistent Green's function formulation and nonlocal effects are fully taken into account. It is shown that impurities modify the linear spectrum and give rise to an impurity band whose position and width depend on the two parameters of our model, the density and the strength of impurities. The presence of the impurity band strongly influences the electromagnetic response and the plasmon losses. Furthermore, we discuss…
We study the effect of a dilute homogeneous spatial distribution of non-magnetic impurities on the equilibrium supercurrent sustained by a ballistic graphene Josephson junction in the short junction limit. Within the Dirac-Bogoliubov-de Gennes approach and modeling impurities by the Anderson model we derive the supercurrent and its equilibrium power spectrum. We find a modification of the current-phase relation with a reduction of the skewness induced by disorder, and a nonmonotonic temperature dependence of the critical current. The potentialities of the supercurrent power spectrum for accura…
It is shown that clustering of charged impurities on graphene can suppress their contribution to the resistivity by a large factor of about the number of impurities per cluster, while leaving the density dependence unchanged. If the cluster size is large in comparison with the Fermi wavelength, the scattering cross section shows sharp resonances as a function of incident angle and electron wavevector. In this regime, due to dominant contribution of scattering by small angles, the transport cross section can be much smaller than the quantum one, which can be verified experimentally by comparing…
We investigate the electrical conductivity of spin-polarized graphene in the presence of short-ranged magnetic scatterers within the relaxation time approximation and the semi-classical Boltzmann approach. Spin-flip scattering of the itinerant electrons from the majority spin sub-band into the minority one results in a minimum in the electrical resistivity at a finite temperature. While this behavior is reminiscent of the renowned Kondo effect, it has an entirely different origin and differs from the Kondo effect in several aspects. In particular, unlike the Kondo effect, this is a single part…
We discuss various scattering mechanisms for Dirac fermions in single-layer graphene. It is shown that scattering on a short-range potential (due to, for example, neutral impurities) is mostly irrelevant for electronic quality of graphene, which is likely to be controlled by charged impurities and ripples (microscopic corrugations of a graphene sheet). The latter are an inherent feature of graphene due to its two-dimensional nature and can also be an important factor in defining the electron mean free path. We show that certain types of ripples create a long-range scattering potential, similar…
It is widely assumed that the dominant source of scattering in graphene is charged impurities in a substrate. We have tested this conjecture by studying graphene placed on various substrates and in high-k media. Unexpectedly, we have found no significant changes in carrier mobility either for different substrates or by using glycerol, ethanol and water as a top dielectric layer. This suggests that Coulomb impurities are not the scattering mechanism that limits the mean free path currently attainable for graphene on a substrate.
We investigate the effects of charged impurity distributions and carrier-carrier interactions on electronic transport in graphene on SiO$_2$ by employing a self-consistent coupled simulation of carrier transport and electrodynamics. We show that impurity clusters of characteristic width 40--50 nm generate electron--hole puddles of experimentally observed sizes. In the conductivity versus carrier density dependence, the residual conductivity and the linear-region slope are determined by the impurity distribution, and the measured slope can be used to estimate the impurity density in experiment.…
We calculate the temperature dependent long-range magnetic coupling in the presence of dilute concentrations of random magnetic impurities in chiral multilayer two-dimensional semimetals, i.e., undoped intrinsic multilayer graphene. Assuming a carrier-mediated indirect RKKY exchange interaction among the well-separated magnetic impurities with the itinerant carriers mediating the magnetic interaction between the impurities, we investigate the magnetic properties of intrinsic multilayer graphene using an effective chiral Hamiltonian model. We find that due to the enhanced density of states in t…
We theoretically study the transport properties of both monolayer and bilayer graphene in the presence of electron-hole puddles induced by charged impurities which are invariably present in the graphene environment. We calculate the graphene conductivity by taking into account the non-mean-field two-component nature of transport in the highly inhomogeneous density and potential landscape, where activated transport across the potential fluctuations in the puddle regimes coexists with regular metallic diffusive transport. The existence of puddles allows the local activation at low carrier densit…
We study the electronic and structural properties of substitutional impurities of graphenelike nanoporous materials C$_2$N, $tg$-, and $hg$-C$_3$N$_4$ by means of density functional theory calculations. We consider four types of impurities; boron substitution on carbon sites (B(C)), carbon substitution on nitrogen sites (C(N)), nitrogen substitution on carbon sites (N(C)), and sulfur substitution on nitrogen sites (S(N)). From cohesive energy calculations, we find that the C(N) and B(C) substitutions are the most energetically favorable and induce small bond modifications in the vicinity of th…
We study both monolayer and bilayer graphene transport properties taking into account the presence of correlations in the spatial distribution of charged impurities. In particular we find that the experimentally observed sublinear scaling of the graphene conductivity can be naturally explained as arising from impurity correlation effects in the Coulomb disorder, with no need to assume the presence of short-range scattering centers in addition to charged impurities. We find that also in bilayer graphene correlations among impurities induce a crossover of the scaling of the conductivity at highe…
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 result, the total interaction energy of randomly distributed impurities embedded in t…
We study the effect of long-range disorder created by charge impurities on the carrier density distribution of graphene-based heterostructures. We consider heterostructures formed by two graphenic sheets (either single layer graphene, SLG, or bilayer graphene, BLG) separated by a dielectric film. We present results for symmetric heterostructures, SLG-SLG and BLG-BLG, and hybrid ones, BLG-SLG. As for isolated layers, we find that the presence of charged impurities induces strong carrier density inhomogeneities, especially at low dopings where the density landscape breaks up in electron-hole pud…
