We present the complete formalism that describes scattering in graphene at low-energies. We begin by analyzing the real-space free Green's function matrix, and its analytical expansions at low-energy, carefully incorporating the discrete lattice structure, and arbitrary forms of the atomic-orbital wave function. We then compute the real-space Green's function in the presence of an impurity. We express our results both in 2X2 and 4X4 forms (for the two sublattices and the two inequivalent valleys of the first Brillouin zone). We compare this with the 4X4 formalism proposed in cond-mat/0608228 and cond-mat/0702019, and show that the latter is incomplete. We describe how it can be adapted to accurately take into account the effects of inter-valley scattering on spatially-varying quantities such as the local density of states.
We study the problem of non-magnetic impurities adsorbed on bilayer graphene in the diluted regime. We analyze the impurity spectral densities for various concentrations and gate fields. We also analyze the effect of the adsorbate on the local density of states (LDOS) of the different C atoms in the structure and present some evidence of strong localization for the electronic states with energies close to the Dirac point.
We study charged impurity scattering and static screening in a top-gated substrate-supported graphene nanostructure. Our model describes how boundary conditions can be incorporated into scattering, sheds light on the dielectric response of these nanostructures, provides insights into the effect of the top gate on impurity scattering, and predicts that the carrier mobility in such graphene heterostructures decreases with increasing top dielectric thickness and higher carrier density. An increase of up to almost 60 percent in carrier mobility in ultrathin top-gated graphene is predicted.
Unique electronic band structure of graphene with its semi-metallic features near the charge neutrality point is sensitive to impurity effects. Using the Lifshitz and Anderson impurity models, we study in detail the disorder induced spectral phenomena in the electronic band structure of graphene, namely, the formation of resonances, quasi-gaps, bound states, impurity sub-bands, and their overall impact on the electronic band restructuring and the associated Mott-like metal-insulator transitions. We perform systematic analytical and numerical study for realistic impurities, both substitutional …
Understanding disorder in graphene is essential for electronic applications; in contrast to conventional materials, the extraordinarily low electron-phonon scattering1, 2 in graphene implies that disorder3-7 dominates its resistivity even at room temperature. Charged impurities5, 8-10 have been identified as an important disorder type in graphene on SiO2 substrates11, 12, giving a nearly linear carrier-density-dependent conductivity σ(n), and producing electron and hole puddles13-15 which determine the magnitude of graphene's minimum conductivity σmin10. Correlations of charged impurities are …
It was found that the spontaneous electric field can occur in doped graphene in an external dc electric field. The direction of the spontaneous field is perpendicular to the applied field. This effect can be connected with the nonequilibrium electron subsystem of graphene. It was also shown up the influence of problem parameters on the characteristics of the spontaneous field.
Anderson impurity problem is considered for a graphene bilayer subject to a gap-opening bias. In-gap localized states are produced even when the impurity level overlaps with the continuum of band electrons. The effect depends strongly on the polarity of the applied bias as long as hybridization with the impurity occurs within a single layer. For an impurity level inside the conduction band a positive bias creates the new localized in-gap state. A negative bias does not produce the same result and leads to a simple broadening of the impurity level. The implications for transport are discussed i…
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…
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.
We use the T-matrix approximation to analyze the effect of a localized impurity on the local density of states in mono- and bilayer graphene. For monolayer graphene the Friedel oscillations generated by intranodal scattering obey an inverse-square law, while the internodal ones obey an inverse law. In the Fourier transform this translates into a filled circle of high intensity in the center of the Brillouin zone, and empty circular contours around its corners. For bilayer graphene both types of oscillations obey an inverse law.
Renowned for its sensitivity to detect the presence of numerous substances, graphene is an excellent chemical sensor. Unfortunately, which general features a dopant must have in order to enter the list of substances detectable by graphene are not exactly known. Here we demonstrate with a simple model calculation implemented in three different ways that one of such features is the symmetry properties of the impurity binding to graphene. In particular, we show that electronic scattering is suppressed when dopants are bound symmetrically to both graphene sub-lattices, giving rise to impurity invi…
We consider a double-layer system made of two parallel bilayer graphene sheets separated by a dielectric medium. We calculate the finite-temperature electrical conductivity of the first layer due to charged impurities located in two layers. We study the effects of temperature, interlayer distance, dielectric constants and impurity concentration, carrier concentration on the electrical conductivity. We show the importance of charged impurities located in layer II in determining electrical conductivity of the first layer for small interlayer distance. The results in this paper give us more under…
We study optically-induced collective excitations of graphene in the presence of a strong perpendicular magnetic field and a single impurity. We determine the energies and absorption strengths of these excitations, which become localised on the impurity. Two different types of impurity are considered i. the long-range Coulomb impurity, ii. a delta-function impurity located at either an A or B graphene sublattice site. Both impurity types result in some bound states appearing both above and below the magnetoplasmon continuum, although the effect of the short-range impurity is less pronounced. T…
We investigate the graphene-impurity interaction problem by combining experimental - scanning tunneling microscopy (STM) and spectroscopy (STS) - and theoretical - Anderson impurity model and density functional theory (DFT) calculations - techniques. We use graphene on the SiC(000-1)(2x2)_C reconstruction as a model system. The SiC substrate reconstruction is based on silicon adatoms. Graphene mainly interacts with the dangling bonds of these adatoms which act as impurities. Graphene grown on SiC(000-1)(2x2)_C shows domains with various orientations relative to the substrate so that very diffe…
The recent experimental study of the far-infrared transmission spectroscopy of monolayer graphene has shown that the Drude peak width increases by more than $10\%$ per $1\%$ of applied mechanical strain, while the Drude weight remains unchanged. We study the influence of the strain on the resonant impurity scattering. We propose a mechanism of augmentation of the scattering rate due to the shift in the position of resonance. Using the Lifshitz model of substitutional impurities, we investigate changes in the Drude peak weight and width as functions of the Fermi energy, impurity concentration a…
We theoretically investigate the impurity levels and exchange interaction between magnetic impurities in graphene driven by an off-resonant circularly polarized light field. Our analysis captures the non-perturbative effects resulting from scattering with magnetic impurities with a strong onsite potential. Under irradiation, a dynamical band gap opens up at the Dirac point, allowing impurity levels to exist inside the gap. These impurity levels are shown to give rise to a resonance feature in the exchange energy for impurities located either at the same or different sublattices. The exchange i…
The interaction between the Fermi sea of conduction electrons and a non-adiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac Fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in a…
The effects of substrate on the electronic properties of Graphene remains unclear. Many theoretical and experimental efforts have been done to clarify this discrepancy. In this work, we studied the electronic transport in armchair Graphene nanoribbons (AGNR) in the presence of substrate's disorder. The three main substrate's disorders -- surface roughness, charged impurity and surface optical phonon -- are investigated. Non-Equilibrium Green's function along with the tight-binding model is employed to investigate the electronic properties of Graphene Nanoribbons. The effects of these disorders…
Electronic transport properties in armchair shaped edges graphene nanoribbons (AGNRs) doped various impurities have been simulated by the non-equilibrium Green's function approach combined with the first principle calculation based on the density functional theory. We have observed that impurity levels appear in electronic struc-tures, and that the quantization of transmission function is moderated for doped AGNRs. The I-V characteristic can be computed from the transmission function. Our simulation results show that AGNRs doped impurities have higher conductance than the non-doped one.
We have examined the impact of charged impurity scattering on charge carrier transport in bilayer graphene (BLG) by deposition of potassium in ultra-high vacuum at low temperature. Charged impurity scattering gives a conductivity which is supra-linear in carrier density, with a magnitude similar to single-layer graphene for the measured range of carrier densities of 2-4 x 10^12 cm^-2. Upon addition of charged impurities of concentration n_imp, the minimum conductivity Sigma_min decreases proportional to n_imp^-1/2, while the electron and hole puddle carrier density increases proportional to n_…
We theoretically revisit graphene transport properties as a function of carrier density, taking into account possible correlations in the spatial distribution of the Coulomb impurity disorder in the environment. We find that the charged impurity correlations give rise to a density dependent graphene conductivity, which agrees well qualitatively with the existing experimental data. We also find, quite unexpectedly, that the conductivity could increase with increasing impurity density if there is sufficient inter-impurity correlation present in the system. In particular, the linearity (sublinear…
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…
The conductivity of armchair graphene nanoribbons in the presence of short-range impurities and edge roughness is studied theoretically using the Boltzmann transport equation for quasi-one-dimensional systems. As the number of occupied subbands increases, the conductivity due to short-range impurities converges towards the two-dimensional case. Calculations of the magnetoconductivity confirm the edge-roughness-induced dips at cyclotron radii close to the ribbon width suggested by the recent quantum simulations.
We report a detailed analytic investigation of the interplay between size quantization and local scattering centers in armchair graphene nanoribbons, as seen in the conductance. The scattering property of a local scattering center is dependent on if it is located on one sublattice (A-site impurity) or both (impurity situated at neighboring carbon atoms, A-B-site impurity). The A-site impurity scatters in a similar way as a localized impurity in a one-dimensional channel made from a two-dimensional electron gas. On the other hand, the A-B-site impurity introduces A- to B-sublattice scattering, …
We theoretically investigate the spin resolved Friedel oscillation (FO) and quasiparticle interference (QPI) in graphene induced by an Anderson impurity. Once the impurity becomes magnetic, the resulted FO becomes spin dependent, which gives rise to a local magnetic moment oscillation with an envelop decaying as $r^{-2}$ in real space in the doping cases. Meanwhile, at half filling, the charge density and local magnetic moment will not oscillate but decay as $r^{-3}$. Such spin resolved FO has both sublattice and spin asymmetry. Interestingly, the local magnetic moment decay at half filling on…
We show that the changes in the electronic density of states (DOS) in graphene induced by impurity scattering with short-range potentials are completely different from those caused by the long-range Coulomb potential. The spectral weight of the state that eventually disappears into the valence band (as the strength of scattering increases) does not transform into a resonance state. Therefore no unusual screening effects related to a redistribution of the density of states in the valence band are observed. The states induced by the short-range impurities in graphene, therefore, have distinctive…
We formulate and solve the perhaps simplest two-body bound state problem for interacting Dirac fermions in two spatial dimensions. A two-body bound state is predicted for gapped graphene monolayers in the presence of weakly repulsive electron-electron interactions and a Coulomb impurity with charge $Ze>0$, where the most interesting case corresponds to $Z=1$. We introduce a variational Chandrasekhar-Dirac spinor wave function and show the existence of at least one bound state. This state leaves clear signatures accessible by scanning tunneling microscopy. One may thereby obtain direct informat…
We investigate time-resolved charge transport through graphene nanoribbons supplemented with adsorbed impurity atoms. Depending on the location of the impurities with respect to the hexagonal carbon lattice, the transport properties of the system may become invisible to the impurity due to the symmetry properties of the binding mechanism. This motivates a chemical sensing device since dopants affecting the underlying sublattice symmetry of the pristine graphene nanoribbon introduce scattering. Using the time-dependent Landauer--B{ü}ttiker formalism, we extend the stationary current-voltage pic…
We calculate the spin-dependent zero-bias conductance $G_{σσ'}$ in armchair graphene nanoribbons with hydrogen adsorbates employing a DFT-based ab initio transport formalism including spin-orbit interaction. We find that the spin-flip conductance $G_{σ\barσ}$ can reach the same order of magnitude as the spin-conserving one, $G_{σσ}$, due to exchange-mediated spin scattering. In contrast, the genuine spin-orbit interaction appears to play a secondary role, only.
The spontaneous self-consistent generation of axial current and corresponding dipole-like magnetic field in a planar electron-positron system similar to graphene and related hetero-structures doped by charged impurity with charge $Z$ is explored. It is shown that this effect takes place for $Z \geq Z^{\ast}$ with $Z^{\ast}$ being a peculiar analogue of the Curie point in ferromagnetics. The properties of induced ferromagnetic state are studied in detail. It is shown also that the arising this way magnetic dipole leads to a significant decrease of the total Casimir (vacuum) energy of the system…
By using Fourier-transform scanning tunneling spectroscopy we measure the interference patterns produced by the impurity scattering of confined Dirac quasiparticles in epitaxial graphene nanoflakes. Upon comparison of the experimental results with tight-binding calculations of realistic model flakes, we show that the characteristic features observed in the Fourier-transformed local density of states are related to scattering between different transverse modes (sub-bands) of a graphene nanoflake and allow direct insight into the electronic spectrum of graphene. We also observe a strong reductio…
The electronic energy spectrum of graphene electron subjected to a homogeneous magnetic field in the presence of a charged Coulomb impurity is studied analytically within two-dimensional Dirac-Weyl picture by using variational approach. The variational scheme we used is just based on utilizing the exact eigenstates of two-dimensional Dirac fermion in the presence of a uniform magnetic field as a basis for determining analytical energy eigenvalues in the presence of an attractive/repulsive charged Coulomb impurity. This approach allows us to determine under which conditions bound state solution…
We theoretically calculate the impurity-scattering induced resistivity of twisted bilayer graphene at low twist angles where the graphene Fermi velocity is strongly suppressed. We consider, as a function of carrier density, twist angle, and temperature, both long-ranged Coulomb scattering and short-ranged defect scattering within a Boltzmann theory relaxation time approach. For experimentally relevant disorder, impurity scattering contributes a resistivity comparable to (much larger than) the phonon scattering contribution at high (low) temperatures. Decreasing twist angle leads to larger resi…
The full counting statistics for the charge transport through an undoped graphene sheet in the presence of strong potential impurities is studied. Treating the scattering off the impurity in the s-wave approximation, we calculate the impurity correction to the cumulant generating function. This correction is universal provided the impurity strength is tuned to a resonant value. In particular, the conductance of the sample acquires a correction of 16e^2/(pi^2 h) per resonant impurity.
We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy bandgap and Landau level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size and magnetic length, we elu…
Resonant scattering at the atomic absorbates in graphene was investigated recently in relation with the transport and gap opening problems. Attaching an impurity atom to graphene is believed to lead to the creation of unusual zero energy localized electron states. This paper aims to describe the behavior of the localized impurity-induced levels in graphene in a quantizing magnetic field. It is shown that in the magnetic field the impurity level effectively hybridizes with one of the n=0 Landau level states and splits into two opposite-energy states. The new hybridized state is doubly occupied,…
Recently, the existence of local magnetic moment in a hydrogen adatom on graphene has been confirmed experimentally [González-Herrero et al., Science, 2016, 352, 437]. Inspired by this breakthrough, we theoretically investigate the top-site adatom on trilayer graphene (TLG) by solving the Anderson impurity model via self-consistent mean field method. The influence of the stacking order, the adsorption site and external electric field are carefully considered. We find that, due to its unique electronic structure, the situation of the TLG is drastically different from that of the monolayer graph…
We show that Friedel oscillations (FO) in grapehene are strongly affected by the chirality of electrons in this material. In particular, the FO of the charge density around an impurity show a faster, $1/r^3$, decay than in conventional 2D electron systems and do not contribute to a linear temperature-dependent correction to the resistivity. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice lead to a negative linear T dependence of the resistivity.
Motivated by quantum chemistry calculations, showing that molecular adsorption in graphene takes place on preferential sites of the honeycomb lattice, we study the effect of an isolated impurity on the local electronic properties of a graphene monolayer, when the impurity is located on a site-like, bond-like, or hollow-like position. We evaluate the local density of states (LDOS) as a function of energy on the impurity and on its neighboring sites, as well as in reciprocal space, at an energy corresponding to a bound state, in the three cases of interest. The latter study may be relevant to in…
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.…
In a recent publication [Phys. Rev. B $\textbf{89}$, 155403 (2014)], the authors investigated the spectrum of a Coulomb impurity in graphene in the presence of magnetic and electric fields using the coupled series expansion approach. In the first part of their publication they investigated how Coulomb impurity states collapse in the presence of a perpendicular magnetic field. We argue that the obtained spectrum does not give information about the atomic collapse and that their interpretation of the spectrum regarding atomic collapse is not correct. We also argue that the obtained results are o…
It is demonstrated that there is a characteristic impurity concentration, at which variation with concentration and overall appearance of the local density of states at the impurity site in graphene are changing their behavior. Features that are prominent in the local density of states for the single impurity are disappearing from it when impurity concentration far exceeds this critical value. The impurity subsystem not only induces the rearrangement of the electron spectrum in graphene, but also undergoes a substantial spectral transformation by itself, which can be observed experimentally.
Experimental evidence from both spin-valve and quantum transport measurements points towards unexpectedly fast spin relaxation in graphene. We report magnetotransport studies of epitaxial graphene on SiC in a vector magnetic field showing that spin relaxation, detected using weak-localisation analysis, is suppressed by an in-plane magnetic field, $B_{\parallel}$, and thereby proving that it is caused at least in part by spinful scatterers. A non-monotonic dependence of effective decoherence rate on $B_{\parallel}$ reveals the intricate role of scatterers' spin dynamics in forming the interfere…
We study graphene which has both spin-orbit coupling (SOC), taken to be of the Kane-Mele form, and a Zeeman field induced due to proximity to a ferromagnetic material. We show that a zigzag interface of graphene having SOC with its pristine counterpart hosts robust chiral edge modes in spite of the gapless nature of the pristine graphene; such modes do not occur for armchair interfaces. Next we study the change in the local density of states (LDOS) due to the presence of an impurity in graphene with SOC and Zeeman field, and demonstrate that the Fourier transform of the LDOS close to the Dirac…
The response of Dirac fermions to a Coulomb potential is predicted to differ significantly from the behavior of non-relativistic electrons seen in traditional atomic and impurity systems. Surprisingly, many key theoretical predictions for this ultra-relativistic regime have yet to be tested in a laboratory. Graphene, a 2D material in which electrons behave like massless Dirac fermions, provides a unique opportunity to experimentally test such predictions. The response of Dirac fermions to a Coulomb potential in graphene is central to a wide range of electronic phenomena and can serve as a sens…
In this review we highlight recent theoretical and experimental work on sublattice asymmetric doping of impurities in graphene, with a focus on substitutional Nitrogen dopants. It is well known that one current limitation of graphene in regards to its use in electronics is that in its ordinary state it exhibits no band gap. By doping one of its two sublattices preferentially it is possible to not only open such a gap, which can furthermore be tuned through control of the dopant concentration, but in theory produce quasi-ballistic transport of electrons in the undoped sublattice, both important…
We study the Fourier transform of the local density of states (LDOS) in graphene in the presence of a single impurity at high magnetic field. We find that the most pronounced features occur for energies of the STM tip matching the Landau level energies. The Fourier transform of the LDOS shows regions of high intensity centered around the center and the corners of the Brillouin zone (BZ). The radial intensity dependence of these features is determined by the form of the wavefunctions of the electrons in the quantum Hall regime. Moreover, some of these regions break rotational symmetry, and thei…
We study the interplay between the edge states and a single impurity in a zigzag graphene nanoribbon. We use tight-binding exact diagonalization techniques, as well as density functional theory calculations to obtain the eigenvalue spectrum, the eigenfunctions, as well the dependence of the local density of states (LDOS) on energy and position. We note that roughly half of the unperturbed eigenstates in the spectrum of the finite-size ribbon hybridize with the impurity state, and the corresponding eigenvalues are shifted with respect to their unperturbed values. The maximum shift and hybridiza…
We present calculations of the thermal and electric linear response in graphene, including disorder in the self-consistent t-matrix approximation. For strong impurity scattering, near the unitary limit, the formation of a band of impurity states near the Fermi level leads to that Mott's relation holds at low temperature. For higher temperatures, there are strong deviations due to the linear density of states. The low-temperature thermopower is proportional to the inverse of the impurity potential and the inverse of the impurity density. Information about impurity scattering in graphene can be …
We present an analytical investigation of the quasi-Coulomb impurity states in a narrow gapped armchair graphene nanoribbon (GNR) in the presence of a uniform external electric field directed parallel to the ribbon axis. The effect of the ribbon confinement is taken to be much greater than that of the impurity electric field, which in turn considerably exceeds the external electric field. Under these conditions we employ the adiabatic approximation assuming that the motion parallel ("slow") and perpendicular ("fast") to the ribbon axis are separated adiabatically. In the approximation of the i…
It is demonstrated that a new nodal point is forming and a domain with anomalous dispersion is unfolding in the spectrum of charge carriers in graphene, when the concentration of weakly bound impurities exceeds a certain critical value.
We report a detailed investigation of the interplay between size quantization and local scattering centers in graphene nanoribbons, as seen in the local density of states. The spectral signatures, obtained after Fourier transformation of the local density of states, include characteristic peaks that can be related to the transverse modes of the nanoribbon. In armchair ribbons, the Fourier transformed density of states of one of the two inequivalent sublattices takes a form similar to that of a quantum channel in a two-dimensional electron gas, modified according to the differences in bandstruc…
We have investigated a new feature of impurity cyclotron resonances common to various localized potentials of graphene. A localized potential can interact with a magnetic field in an unexpected way in graphene. It can lead to formation of anomalous boundstates that have a sharp peak with a width $R$ in the probability density inside the potential and a broad peak of size magnetic length $\ell$ outside the potential. We investigate optical matrix elements of anomalous states, and find that they are unusually small and depend sensitively on magnetic field. The effect of many-body interactions on…
We report the observation of an isolated charged impurity in graphene and present direct evidence of the close connection between the screening properties of a 2D electron system and the influence of the impurity on its electronic environment. Using scanning tunneling microscopy and Landau level spectroscopy we demonstrate that in the presence of a magnetic field the strength of the impurity can be tuned by controlling the occupation of Landau-level states with a gate-voltage. At low occupation the impurity is screened becoming essentially invisible. Screening diminishes as states are filled u…
We study the effect of resonant scatterers on the local density of states in a rectangular graphene setup with metallic leads. We find that the density of states in a vicinity of the Dirac point acquires a strong position dependence due to both metallic proximity effect and impurity scattering. This effect may prevent uniform gating of weakly-doped samples. We also demonstrate that even a single-atom impurity may essentially alter electronic states at low-doping on distances of the order of the sample size from the impurity.
We study the localized magnetic states of impurity in biased bilayer and trilayer graphene. It is found that the magnetic boundary for bilayer and trilayer graphene presents the mixing features of Dirac and conventional fermion. For zero gate bias, as the impurity energy approaches the Dirac point, the impurity magnetization region diminishes for bilayer and trilayer graphene. When a gate bias is applied, the dependence of impurity magnetic states on the impurity energy exhibits a different behavior for bilayer and trilayer graphene due to the opening of a gap between the valence and the condu…
We consider the nonlinear terahertz response of n-doped monolayer graphene at room temperature using a microscopic theory of carrier dynamics. Our tight-binding model treats the carrier-field interaction in the length gauge, includes phonon as well as short-range neutral-impurity scattering, and fully accounts for the intrinsic nonlinear response of graphene near the Dirac point. Treating each interaction microscopically allows us to separate contributions from current clipping, phonon creation, and elastic impurity scattering. Although neutral impurity scattering and phonon scattering are bot…
Both transport $τ_{tr}$ and elastic scattering times $τ_{e}$ are experimentally determined from the carrier density dependence of the magnetoconductance of monolayer and bilayer graphene. Both times and their dependences in carrier density are found to be very different in the monolayer and the bilayer. However their ratio $τ_{tr}/τ_{e} $is found to be of the order of $1.5 $ in both systems and independent of the carrier density. These measurements give insight on the nature (neutral or charged) and spatial extent of the scattering centers. Comparison with theoretical predictions yields that t…
