We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green's function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green's function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.
We calculate the dynamical polarization function and solve a self-consistent gap equation in the random phase approximation in undoped ABC-stacked n-layer graphene. We find that the gap is maximal in trilayer graphene and decreases monotonously for $n \ge 4$ because the effects of screening in the gap equation win over those connected with the flattening of electron bands as n increases.
In this comment we show that some equations and results of the paper titled "Dielectric screening and plasmons in AA-stacked bilayer graphene" are not correct. Furthermore, we present our results which seems to be more correct.
The influence of screening on the condensed state of bilayer graphene is studied within the framework of the Thomas Fermi approximation. We find that screening has little effect on the Kosterlitz-Thouless temperature in the strongly interacting regime. Furthermore, we predict that the phase transition to the condensed state is first order.
We have investigated the Coulomb screening properties and collective excitations in a graphene bilayer. The static screening effect is anisotropic and is much stronger in the undoped graphene bilayer than in a monolayer graphene [1]. The dynamic screening shows the properties of a Dirac gas in the low frequency and that of a Fermi gas in the high frequency. The transition from the Dirac to the Fermi gas is also observed in the plasmon spectrum. Finally, we find that an electron gas in a doped graphene bilayer has quite similar properties as those of a Fermi gas in materials containing two ener…
We discuss the physics of the tunable bandgap in bilayer graphene with the gate voltage and doping. A comparison with experimental data obtained by Kuzmenko et al [Phys. Rev. B \textbf{80}, 165406 (2009)] demonstrates the good agreement.
We calculate the static polarizability of multilayer graphene and study the effect of stacking arrangement, carrier density, and onsite energy difference on graphene screening properties. At low densities, the energy spectrum of multilayer graphene is described by a set of chiral two-dimensional electron systems and the associated chiral nature determines the screening properties of multilayer graphene showing very different behavior depending on whether the chirality index is even or odd. As density increases, the energy spectrum follows that of the monolayer graphene and thus the polarizabil…
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.
Screening is one of the fundamental concepts in solid state physics. It has a great impact on the electronic properties of graphene where huge mobilities were observed in spite of the large concentration of charged impurities. While static screening has successfully explained DC mobilities, screening properties can be significantly changed at infrared or optical frequencies. In this paper we discuss the influence of dynamical screening on the optical absorption of graphene and other 2D electron systems like metallic monolayers. This research is motivated by recent experimental results which po…
We report on Coulomb blockade and Coulomb diamond measurements on an etched, tunable single-layer graphene quantum dot. The device consisting of a graphene island connected via two narrow graphene constrictions is fully tunable by three lateral graphene gates. Coulomb blockade resonances are observed and from Coulomb diamond measurements a charging energy of ~3.5 meV is extracted. For increasing temperatures we detect a peak broadening and a transmission increase of the nanostructured graphene barriers.
The charge distribution induced by external fields in finite stacks of graphene planes, or in semiinfinite graphite is considered. The interlayer electronic hybridization is described by a nearest neighbor hopping term, and the charge induced by the self consistent electrostatic potential is calculated within linear response (RPA). The screening properties are determined by contributions from inter- and intraband electronic transitions. In neutral systems, only interband transitions contribute to the charge polarizability, leading to insulating-like screening properties, and to oscillations in…
We present a non-linear Thomas-Fermi theory which describes the electric charge screening in the system including two charged substrate layers separated by a few-layered graphene film. We show that by increasing the charge at the interfaces, the system could be turned from the weak screening regime where the whole film responds to the external charge, to the strong screening regime where the external charge is screened by a surface charge distribution confined to the bounding graphene layers. The transition from weak to strong screening is shown to turn on relatively quickly, and it happens wh…
Boltzmann diffusive transport including relaxation time and mobility in graphene limited by ionized impurity scattering is investigated. The relaxation time is evaluated with two different methods, first one directly use Boltzmann transport equation via scattering matrix, second one is based on scattering cross-section. Two methods yield the same relaxation time results for graphene. Assume linear Thomas-Fermi screening and a reasonable electron carrier density, relaxation time and mobility can be calculated and plotted, which demonstrates graphene is a very promising high mobility material fo…
A fully selfconsistent treatment for gap generation and Coulomb screening in excitonic insulators is presented. The method is based on the equations of motion for the relevant dynamical variables combined with a variational approach. Applying the theory for a model system of bilayer graphene, an excitonic groundstate with a gap exceeding 10 meV is predicted.
Electrons in two-dimensional graphene sheets behave as interacting chiral Dirac fermions and have unique screening properties due to their symmetry and reduced dimensionality. By using a combination of scanning tunneling spectroscopy (STM/STS) measurements and theoretical modeling we have characterized how graphene's massless charge carriers screen individual charged calcium atoms. A back-gated graphene device configuration has allowed us to directly visualize how the screening length for this system can be tuned with carrier density. Our results provide insight into electron-impurity and elec…
We study the effect of perpendicular electric fields on the band structures of ABA and ABC graphene multilayers, and find that the electronic screening effect is significantly different between them. In ABA multilayers, the field produces a band overlap and gives a linear screening, while in ABC multilayers, in contrast, it opens an energy gap in the surface-state band at low energy, leading to a strong screening effect essentially non-linear to the field amplitude. The energy gap of a large ABC stack sharply rises when the external field exceeds a certain critical value.
We study the static and dynamic screening of gapped bilayer graphene. Unlike previous works we use the 4-band model instead of the simplified 2-band model. We find that there are important qualitative differences between the dielectric screening function obtained using the 2-band and that obtained using the 4-band model. In particular within the 4-band model in the presence of a band-gap the static screening exhibits Kohn anomalies that are absent within the 2-band model. Moreover, using the 4-band model, we are able to examine the effect of trigonal warping (absent in the 2-band model) on the…
Screening of a large external charge in graphene is studied. The charge is assumed to be displaced away or smeared over a finite region of the graphene plane. The initial decay of the screened potential with distance is shown to follow the 3/2 power. It gradually changes to the Coulomb law outside of a hypercritical core whose radius is proportional to the external charge.
We have investigated the Coulomb screening properties and plasmon spectrum in a bilayer graphene under a perpendicular electric bias. The bias voltage applied between the two graphene layers opens a gap in the single particle energy spectrum and modifies the many-body correlations and collective excitations. The energy gap can soften the plasmon modes and lead to a crossover of the plasmons from a Landau damped mode to being undamped. Plasmon modes of long lifetime may be observable in experiments and may have potentials for device applications.
Electromagnetic fields bound tightly to charge carriers in a two-dimensional sheet, namely surface plasmons, are shielded by metallic plates that are a part of a device. It is shown that for epitaxial graphenes, the propagation velocity of surface plasmons is suppressed significantly through a partial screening of the electron charge by the interface states. On the basis of analytical calculations of the electron lifetime determined by the screened Coulomb interaction, we show that the screening effect gives results in agreement with those of a recent experiment.
The effect of charge-carrier screening on the transport properties of a neutral graphene sheet is studied by directly probing its electronic structure. We find that the Fermi velocity, Dirac point velocity, and overall distortion of the Dirac cone are renormalized due to the screening of the electron-electron interaction in an unusual way. We also observe an increase of the electron mean free path due to the screening of charged impurities. These observations help us to understand the basis for the transport properties of graphene, as well as the fundamental physics of these interesting electr…
We study the charge density distribution, the electric field profile, and the resistance of an electrostatically created lateral p-n junction in graphene. We show that the electric field at the interface of the electron and hole regions is strongly enhanced due to limited screening capacity of Dirac quasiparticles. Accordingly, the junction resistance is lower than estimated in previous literature.
We calculate the screening function in bilayer graphene (BLG) both in the intrinsic (undoped) and the extrinsic (doped) regime within random phase approximation, comparing our results with the corresponding single layer graphene (SLG) and the regular two dimensional electron gas (2DEG). We find that the Kohn anomaly is strongly enhanced in BLG. We also discuss the Friedel oscillation and the RKKY interaction, which are associated with the non-analytic behavior of the screening function at $q=2k_F$. We find that the Kohn anomaly, the Friedel oscillation, and the RKKY interaction are all qualita…
With the motivation of improving the performance and reliability of aggressively scaled nano-patterned graphene field-effect transistors, we present the first systematic experimental study on charge and current distribution in multilayer graphene field-effect transistors. We find a very particular thickness dependence for Ion, Ioff, and the Ion/Ioff ratio, and propose a resistor network model including screening and interlayer coupling to explain the experimental findings. In particular, our model does not invoke modification of the linear energy-band structure of graphene for the multilayer c…
We describe scanning tunneling spectroscopy (STS) measurements performed on individual cobalt (Co) atoms deposited onto backgated graphene devices. We find that Co adatoms on graphene can be ionized by either the application of a global backgate voltage or by the application of a local electric field from a scanning tunneling microscope (STM) tip. Large screening clouds are observed to form around Co adatoms ionized in this way, and we observe that some intrinsic graphene defects display a similar behavior. Our results provide new insight into charged impurity scattering in graphene, as well a…
Generation of high harmonics in a monolayer graphene initiated by strong coherent radiation field, taking into account electron-electron Coulomb interaction is investigated. A microscopic theory describing the nonlinear optical response of graphene is developed. The Coulomb interaction of electrons is treated in the scope of dynamic Hartree-Fock approximation. The closed set of integrodifferential equations for the single-particle density matrix of a graphene quantum structure is solved numerically. The obtained solutions show the significance of many-body Coulomb interaction on the high harmo…
We present a theory of the influence of band renormalization and excitonic electron-electron interaction effects on the optical conductivity $σ(ω)$ of doped bilayer graphene. Using the Keldysh formalism, we derive a kinetic equation from which we extract numerical and approximate analytic results for $σ(ω)$. Our calculations reveal a previously unrecognized mechanism which couples the Drude and interband response and renormalizes the plasmon frequency, and suggest that screening must play an essential role in explaining the weakly renormalized conductivity seen in recent experiments.
The orbital magnetism in spatially varying magnetic fields is studied in monolayer graphene within the effective mass approximation. We find that, unlike the conventional two-dimensional electron system, graphene with small Fermi wave number k_F works as a magnetic shield where the field produced by a magnetic object placed above graphene is always screened by a constant factor on the other side of graphene. The object is repelled by a diamagnetic force from the graphene, as if there exists its mirror image with a reduced amplitude on the other side of graphene. The magnitude of the force is m…
We consider the effect of periodic scalar and vector potentials generated by periodic deformations of the graphene crystal lattice, on the energy spectrum of electrons. The dependence of electron velocity near the Dirac point on the periodic perturbations of different types is discussed. We also investigated the effect of screening of the scalar potential by calculating the dielectric function as a function of the wave length of the periodic potential. This calculation shows that the periodic scalar field is strongly suppressed by the screening. Using the dependence of electron velocity on the…
Electron interactions in undoped bilayer graphene lead to instability of the gapless state, `which-layer' symmetry breaking, and energy gap opening at the Dirac point. In contrast to single layer graphene, the bilayer system exhibits instability even for arbitrarily weak interaction. A controlled theory of this instability for realistic dynamically screened Coulomb interactions is developed, with full acount of dynamically generated ultraviolet cutoff. This leads to an energy gap that scales as a power law of the interaction strength, making the excitonic instability readily observable.
We analyze the response of bilayer graphene to an external transverse electric field using a variational method. A previous attempt to do so in a recent paper by Falkovsky [Phys. Rev. B 80, 113413 (2009)] is shown to be flawed. Our calculation reaffirms the original results obtained by one of us [E. McCann, Phys. Rev. B 74, 161403(R) (2006)] by a different method. Finally, we generalize these original results to describe a dual-gated bilayer graphene device.
We have studied the dielectric screening of electric field which is induced by a gate voltage in twisted double bilayer graphene by using a sample with a mismatch angle of about 5 degrees. In low temperature magnetotransport measurements, quantum oscillations of magnetoresistance originating from two bands with different carrier density were observed. The behavior of the carrier densities with respect to the total carrier density were distinct from that of the AB-stacked tetralayer graphene. The carrier density ratio was theoretically analyzed in terms of the model that the induced charge deca…
Liquid-based applications of biomolecule-decorated field-effect transistors (FETs) range from biosensors to in vivo implants. A critical scientific challenge is to develop a quantitative understanding of the gating effect of charged biomolecules in ionic solution and how this influences the readout of the FETs. To address this issue, we fabricated protein-decorated graphene FETs and measured their electrical properties, specifically the shift in Dirac voltage, in solutions of varying ionic strength. We found excellent quantitative agreement with a model that accounts for both the graphene pola…
The screening properties and collective excitations (plasmons) in AA-stacked bilayer graphene are studied within the random phase approximation (RPA). Whereas long lived plasmons in single layer graphene and in AB-stacked bilayer graphene can exist only in doped samples, we find that coherent plasmons can disperse in AA-stacked bilayer graphene {\it even in the absence of doping}. Moreover, we show that the characteristic low energy dispersion relation is unaffected by changes in the number of carriers, unless the chemical potential of the doped sample exceeds the inter-layer hopping energy. W…
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 calculate electron-hole generation and recombination rates for Coulomb scattering (Auger recombination and impact ionization) in Graphene. The conduction and valence band dispersion relation in Graphene together with energy and momentum conservation requirements restrict the phase space for Coulomb scattering so that electron-hole recombination times can be much longer than 1 ps for electron-hole densities smaller than $10^{12}$ cm$^{-2}$.
We study the conductance spectrum of graphene quantum dots, both single and multiple cases. The single electron tunneling phenomenon is investigated and the periodicity, amplitude and line shape of the Coulomb blockade oscillations at low temperatures are obtained. Further, we discuss the transport behavior when multiple dots are assembled in array and find a phase transition of conductance spectra from individual Coulomb blockade to collective Coulomb blockade.
We study the Coulomb drag transresistivity between graphene layers employing the finite temperature density response function. We analyze the Coulomb coupling between the two layers and show that a universal scaling behavior, independent of the interlayer distance can be deduced. We argue that this universal behavior may be experimentally observable in a system of two carbon nanotubes of large radius.
Using a novel structure, consisting of two, independently contacted graphene single layers separated by an ultra-thin dielectric, we experimentally measure the Coulomb drag of massless fermions in graphene. At temperatures higher than 50 K, the Coulomb drag follows a temperature and carrier density dependence consistent with the Fermi liquid regime. As the temperature is reduced, the Coulomb drag exhibits giant fluctuations with an increasing amplitude, thanks to the interplay between coherent transport in the graphene layer and interaction between the two layers.
We calculate the static polarization of AAA-stacked trilayer graphene (TLG) and study its screening properties within the random phase approximation (RPA) in all undoped, doped and biased regimes. We find that the static polarization of undoped AAA-stacked TLG is a combination of the doped and undoped single layer graphene static polarization. This leads to an enhancement of the dielectric background constant along a Thomas-Fermi screening with the Thomas-Fermi wave vector which is independent of carrier concentrations and a 1/r^3 power law decay for the long-distance behavior of the screened …
The use of a nearby metallic ground-plane to limit the range of the Coulomb interactions between carriers is a useful approach in studying the physics of two-dimensional (2D) systems. This approach has been used to study Wigner crystallization of electrons on the surface of liquid helium, and most recently, the insulating and metallic states of semiconductor-based two-dimensional systems. In this paper, we perform calculations of the screening effect of one 2D system on another and show that a 2D system is at least as effective as a metal in screening Coulomb interactions. We also show that th…
We present transport measurements on a tunable three-layer graphene single electron transistor (SET). The device consists of an etched three-layer graphene flake with two narrow constrictions separating the island from source and drain contacts. Three lateral graphene gates are used to electrostatically tune the device. An individual three-layer graphene constriction has been investigated separately showing a transport gap near the charge neutrality point. The graphene tunneling barriers show a strongly nonmonotonic coupling as function of gate voltage indicating the presence of localized stat…
I suggest to use the effect of Coulomb drag between two closely positioned graphite monolayers (graphene sheets) for experimental measurement of the strength of weak non-linearities of the spectrum in graphene. I consider trigonal warping as a representative mechanism responsible for the drag effect. Since graphene is relatively defect-free, I evaluate the drag conductivity in the ballistic regime and find that it is proportional to the fourth power of the warping strength.
Magnetoplasmons on graphene edge in quantizing magnetic field are investigated at different Landau level filling factors. To find the mode frequency, the optical conductivity tensor of disordered graphene in magnetic field is calculated in the self-consistent Born approximation, and the nonlocal electromagnetic problem is solved using the Wiener-Hopf method. Magnetoplasmon dispersion relations, velocities and attenuation lengths are studied numerically and analytically with taking into account the screening by metallic gate and the energy dissipation in graphene. The magnetoplasmon velocity de…
Kohn anomalies in three-dimensional metallic crystals are dips in the phonon dispersion that are caused by abrupt changes in the screening of the ion-cores by the surrounding electron-gas. These anomalies are also present at the high-symmetry points Γand K in the phonon dispersion of two-dimensional graphene, where the phonon wave-vector connects two points on the Fermi surface. The linear slope around the kinks in the highest optical branch is proportional to the electron-phonon coupling. Here, we present a combined theoretical and experimental study of the influence of the dielectric substra…
We address the intrinsic polarisation and screening of external electric field in a broad range of ordered and twisted configurations of multilayer graphene, using an ab initio approach combining density functional theory and the Wannier function formalism. We show that multilayer graphene is intrinsically polarized due to the crystal field effect, an effect that is often neglected in tight-binding models of twisted bilayer graphene and similar systems. This intrinsic polarization of the order of up to few tens of meVs has different out-of-plane alignments in ordered and twisted graphene multi…
We have theoretically studied the collective response properties of the two-dimensional chiral electron gas in bilayer graphene within the random phase approximation. The cooperation of external controlling factors like perpendicular electric bias, temperature, doping, and substrate background provides great freedom to manipulate the dynamic dielectric function and the low-energy plasmon dispersion of the system. Intriguing situations with potential application are systematically explored and discussed. Extra undamped plasmon modes might emerge under electric bias. They have almost zero group …
We suggest a simple model of disorder in graphene assuming that there are randomly distributed positive and negative centers with equal concentration $N/2$ in the bulk of silicon oxide substrate. We show that at zero gate voltage such disorder creates two-dimensional concentration $n_0 \sim N^{2/3}$ of electrons and holes in graphene. Electrons and holes reside in alternating in space puddles of the size $R_0 \sim N^{-1/3}$. A typical puddle has only one or two carriers in agreement with recent scanning single electron transistor experiment.
We show that Coulomb drag in ultra-clean graphene double layers can be used for controlling the on/off ratio for current flow by tunning the external gate voltage. Hence, although graphene remains semi-metallic, the double layer graphene system can be tuned from conductive to a highly resistive state. We show that our results explain previous data of Coulomb drag in double layer graphene samples in disordered SiO2 substrates.
We propose that recent transport experiments revealing the existence of an energy gap in graphene nanoribbons may be understood in terms of Coulomb blockade. Electron interactions play a decisive role at the quantum dots which form due to the presence of necks arising from the roughness of the graphene edge. With the average transmission as the only fitting parameter, our theory shows good agreement with the experimental data.
We solve a nonlinear integral equation for the electrostatic potential in doped graphene due to an external charge, arising from a Thomas-Fermi (TF) model for screening by graphene's $π$ electron bands. In particular, we study the effects of a finite equilibrium charge carrier density in graphene, non-zero temperature, non-zero gap between graphene and a dielectric substrate, as well as the nonlinearity in the band density of states. Effects of the exchange and correlation interactions are also briefly discussed for undoped graphene at zero temperature. Nonlinear results are compared with both…
Electron-electron interactions play a critical role in many condensed matter phenomena, and it is tempting to find a way to control them by changing the interactions' strength. One possible approach is to place a studied system in proximity of a metal, which induces additional screening and hence suppresses electron interactions. Here, using devices with atomically-thin gate dielectrics and atomically-flat metallic gates, we measure the electron-electron scattering length in graphene and report qualitative deviations from the standard behavior. The changes induced by screening become important…
Resonant scatterers such as hydrogen adatoms can strongly enhance the low energy density of states in graphene. Here, we study the impact of these impurities on the electronic screening. We find a two-faced behavior: Kubo formula calculations reveal an increased dielectric function $\varepsilon$ upon creation of midgap states but no metallic divergence of the static $\varepsilon$ at small momentum transfer $q\to 0$. This bad metal behavior manifests also in the dynamic polarization function and can be directly measured by means of electron energy loss spectroscopy. A new length scale $l_c$ bey…
In this article we study the static polarization in ABC-stacked multilayer graphene. Since the density of states diverges for these systems if the number of layers exceeds three, screening effects are expected to be important. In the random phase approximation, screening can be included through the polarization. We derive an analytical integral expression for the polarization in both the full-band model and an effective two-band model. Numerical evaluation of these integrals are very time consuming in the full-band model. Hence, for ABC-stacked trilayer graphene, we use the two-band model to c…
The excitation spectrum and the collective modes of graphene antidot lattices (GALs) are studied in the context of a $π$-band tight-binding model. The dynamical polarizability and dielectric function are calculated within the random phase approximation. The effect of different kinds of disorder, such as geometric and chemical disorder, are included in our calculations. We highlight the main differences of GALs with respect to single-layer graphene (SLG). Our results show that, in addition to the well-understood bulk plasmon in doped samples, inter-band plasmons appear in GALs. We further show …
The ability to control the strength of interaction is essential for studying quantum phenomena emerging from a system of correlated fermions. For example, the isotope effect illustrates the effect of electron-phonon coupling on superconductivity, providing an important experimental support for the BCS theory. In this work, we report a new device geometry where the magic-angle twisted bilayer graphene (tBLG) is placed in close proximity to a Bernal bilayer graphene (BLG) separated by a 3 nm thick barrier. Using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb …
We recently introduced a method based on density functional theory (DFT) and non-equilibrium Green's function techniques (NEGF) for calculating the addition energies of single molecule nano-junctions in the Coulomb blockade (CB) regime. Here we apply this approach to benzene molecules lying parallel and at various distances from two aluminum fcc (111) surfaces, and discuss the distance dependence in our calculations in terms of electrostatic screening effects. The addition energies near the surface are reduced by about a factor of two, which is comparable to previously reported calculations em…
