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.
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…
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 …
Ground-state of graphene in the presence of random charged impurities
我们计算的载流子密度依赖的基态性能的石墨烯在衬底中的随机带电杂质的存在下，考虑到无序和相互作用的影响，在一个自洽的理论形式主义的平等的基础上非微扰。我们提供了详细的定量结果上的依赖性的无序引起的空间不均匀的二维载流子密度分布的外部栅极偏置，杂质密度，和杂质的位置。我们发现，无序和相互作用之间的相互作用是强烈的，特别是在较低的杂质密度。我们表明，对于目前可用的典型石墨烯样品，在低（$\lesssim 10^{12}$ cm $^{-2}$）载流子密度下，不均匀性主导石墨烯物理，密度波动变得大于平均密度。
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.
We demonstrate that a giant spin Hall effect (SHE) can be induced by introducing a small amount of Bi impurities in Cu. Our analysis based on a new 3-dimensional finite element treatment of spin transport shows that the sign of the SHE induced by the Bi impurities is negative and its spin Hall (SH) angle amounts to -0.24. Such a negative large SH angle in CuBi alloys can be explained by applying the resonant scattering model proposed by Fert and Levy [Phys. Rev. Lett. 106, 157208 (2011)] to 6p impurities.
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…
Results of first principles modelling of interactions graphene and graphite with iron impurities predict the colossal difference between these two carbon allotropes. Insertion of the iron atoms between the planes of graphite is much more energetically favourable than adsorption of the iron adatom at graphite or graphene surface. High mobility of iron adatom over graphite surface and within bulk graphite is reported. Calculated values of formation energies for the substitutional iron impurities suggest that iron is more destructive for graphite than for graphene. This effect caused formation of…
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 …
We evaluate the autocorrelation function of the electrostatic potential in doped graphene due to nearby charged impurities. The screening of those impurities is described by a combination of the polarization function for graphene in random phase approximation with the electrostatic Green's function of the surrounding dielectrics. Using the hard-disk model for a two-dimensional distribution of impurities, we show that large correlation lengths between impurities can give rise to anti-correlation in the electrostatic potential, in agreement with recent experiments.
We describe the structural and electronic properties of graphene doped with substitutional impurities of 4d and 5d transition metals. The binding energy and distances for 4d and 5d metals in graphene show similar trends for the later groups in the periodic table, which is also well-known characteristic of 3d elements. However, along earlier groups the 4d impurities in graphene show very similar binding energies, distances and magnetic moments to 5d ones, which can be related to the influence of the 4d and 5d lanthanide contraction. Surprisingly, within the manganese group, the total magnetic m…
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…
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 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…
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 …
We directly visualize the three-dimensional (3D) geometry and dynamics of silicon impurities in graphene as well as their dynamics by aberration-corrected scanning transmission electron microscopy. By acquiring images when the sample is tilted, we show that an asymmetry of the atomic position of the heteroatom in the projection reveals the non-planarity of the structure. From a sequence of images, we further demonstrate that the Si atom switches between up- and down- configurations with respect to the graphene plane, with an asymmetric cross-section. We further analyze the 3D structure and dyn…
The growth of graphene on copper by atmospheric pressure chemical vapor deposition in a system free of pumping equipment is investigated. The emphasis is put on the necessity of hydrogen presence during graphene synthesis and cooling. In the absence of hydrogen during the growth step or cooling at slow rate, weak carbon coverage, consisting mostly of oxidized and amorphous carbon, is obtained on the copper catalyst. The oxidation originates from the inevitable occurrence of residual oxidizing impurities in the reactor's atmosphere. Graphene with appreciable coverage can be grown within the vac…
Motivated by experiments on ion irradiated graphene, we compute the resistivity of graphene with dilute impurities. In the local moment regime we employ the perturbation theory up to third order in the exchange coupling to determine the behavior at high temperatures within the Kondo model. Resistivity due to charge fluctuations is obtained within the mean field approach on the Anderson impurity model. Due to the linear spectrum of the graphene the Kondo behavior is shown to depend on the gate voltage applied. The location of the impurity on the graphene sheet is an important variable determini…
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 (…
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 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…
Pristine graphene and graphene-based heterostructures exhibit exceptionally high electron mobility and conductance if their surface contains few electron-scattering impurities. Here, we reveal a universal connection between graphene's carrier mobility and the variation of its electrical conductance with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which reproduces the observed universality. Taking a single conductance measurement as input, this model accurately predicts the full shape of the conductance versus carrier den…
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 the band dispersion of graphene with randomly distributed structural defects using two complementary methods, exact diagonalization of the tight-binding Hamiltonian and implementing a self-consistent T matrix approximation. We identify three distinct types of impurities resulting in qualitatively different spectra in the vicinity of the Dirac point. First, resonant impurities, such as vacancies or 585 defects, lead to stretching of the spectrum at the Dirac point with a finite density of localized states. This type of spectrum has been observed in epitaxial graphene by photoemission s…
We study rectangular graphene flakes using mean field states as the basis for a configuration interaction calculation, which allows us to analyze the low lying electronic excited states including electron correlations beyond the mean field level. We find that the lowest energy transition is polarized along the long axis of the flake, but the charge distributions involved in these transitions are invariably localized on the zigzag edges. We also investigate the impact of both short and long range impurity potentials on the optical properties of these systems. We predict that even a weak impurit…
Graphene is an attractive material for microelectronics applications, given such favourable electrical characteristics as high mobility, high operating frequency, and good stability. If graphene is to be implemented in electronic devices on a mass scale, then it must be compatible with existing semiconductor industry fabrication processes. Unfortunately, such processing introduces defects and impurities to the graphene, which cause scattering of the charge carriers and changes in doping level. Scattering results in degradation of electrical performance, including lower mobility and Dirac point…
Taking into account the possibility of a p-wave hybridization function $V(\vec k)$ of ad-atom with Dirac electrons in graphene -- which arises for vacancies and hollow-site impurities -- we study the nature of magnetic moment formation within the single impurity Anderson model (SIAM). Compared to the s-wave hybridization function, we find that the local moments formed within the Hartree mean field are robust against the change in the parameters of the model. Further we investigate the stability of the local moments with respect to quantum fluctuations by going beyond the Hartree approximation.…
Motivated by the experimental measurement of electrical and hall conductivity, thermopower and Nernst effect, we calculate the longitudinal and transverse electrical and heat transport in graphene in the presence of unitary scatterers as well as charged impurities. The temperature and carrier density dependence in this system display a number of anomalous features that arise due to the relativistic nature of the low energy fermionic degrees of freedom. We derive the properties in detail including the effect of unitary and charged impurities self-consistently, and present tables giving the anal…
The formation energies for mono- and bivacancies in graphene in the presence of adatoms of various metals and small metallic clusters have been calculated. It is shown that transition metal impurities, such as iron, nickel and, especially, cobalt reduce dramatically the vacancy formation energies whereas gold impurities have almost no effect on characteristics of the vacancies. This results highlight that special measures are required in order to protect graphene from damage by transition metal leads.
We present measurements of the Spin Hall Effect (SHE) in AuW and AuTa alloys for a large range of W or Ta concentrations by combining experiments on lateral spin valves and Ferromagnetic-Resonance/spin pumping technique. The main result is the identification of a large enhancement of the Spin Hall Angle (SHA) by the side-jump mechanism on Ta impurities, with a SHA as high as + 0.5 (i.e $50\%$) for about 10\% of Ta. In contrast the SHA in AuW does not exceed + 0.15 and can be explained by intrinsic SHE of the alloy without significant extrinsic contribution from skew or side-jump scattering by …
最近的悬浮石墨烯实验显示载流子迁移率高达200，000 cm^2/Vs，受此启发，我们假设库仑杂质为主要散射机制，从理论上计算了输运性质。我们认为，在扩散机制中进行的无衬底实验与我们的理论一致，并验证了我们早期的许多预测，包括（i）去除衬底将增加迁移率，因为大多数带电杂质都在衬底中，（ii）最小电导率不是通用的，而是取决于杂质浓度，更清洁的样品具有更高的最小电导率。我们进一步认为，悬浮石墨烯上的实验对我们的理论中涉及的两个参数，即带电杂质浓度n_imp和d，带电杂质与石墨烯片的典型距离，施加了很强的约束。最近对悬浮石墨烯的实验表明，与SiO_2衬底上石墨烯的杂质密度约为10^{12} cm ^{-2}相比，可能粘附在石墨烯界面上的残留杂质密度为1-2 \times 10 ^{10} cm ^{-2}。因此，传输实验可以用作光谱工具来识别悬浮石墨烯中剩余杂质的性质。
We investigate the interactions between two identical magnetic impurities substituted into a graphene superlattice. Using a first-principles approach, we calculate the electronic and magnetic properties for transition-metal substituted graphene systems with varying spatial separation. These calculations are compared for three different magnetic impurities, manganese, chromium, and vanadium. We determine the electronic band structure, density of states, and Millikan populations (magnetic moment) for each atom, as well as calculate the exchange parameter between the two magnetic atoms as a funct…
Motivated by recent studies reporting the formation of localized magnetic moments in doped graphene, we investigate the energetic cost for spin polarizing isolated impurities embedded in this material. When a well-known criterion for the formation of local magnetic moments in metals is applied to graphene we are able to predict the existence of magnetic moments in cases that are in clear contrast to previously reported Density Functional Theory (DFT) results. When generalized to periodically repeated impurities, a geometry so commonly used in most DFT-calculations, this criterion shows that th…
We show, both experimentally and theoretically, a novel route to obtain giant room temperature spin Hall effect due to surface-assisted skew scattering. In the experiment, we report the spin Hall effect in Pt-doped Au films with different thicknesses $t_N$. The giant spin Hall angle $γ_S$ = $0.12 \pm 0.04$ is obtained for $t_N$ = 10 nm at room temperature, while it is much smaller for $t_N$ = 20 nm sample. Combined ab initio and quantum Monte Carlo calculations for the skew scattering due to a Pt impurity show $γ_S$ $\cong$ 0.1 on the Au (111) surface, while it is small in bulk Au. The quantum…
