Tuning the effective fine structure constant in graphene: opposing effects of dielectric screening on short- and long-range potential scattering

We reduce the dimensionless interaction strength alpha in graphene by adding a water overlayer in ultrahigh vacuum, thereby increasing dielectric screening. The mobility limited by long-range impurity scattering is increased over 30%, due to the background dielectric constant enhancement leading to a reduced interaction of electrons with charged impurities. However, the carrier-density-independent conductivity due to short-range impurities is decreased by almost 40%, due to reduced screening of the impurity potential by conduction electrons. The minimum conductivity is nearly unchanged, due to canceling contributions from the electron-hole puddle density and long-range impurity mobility. Experimental data are compared with theoretical predictions with excellent agreement.     

Theory of charged impurity scattering in two-dimensional graphene

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 and 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.     

Conductance of metallic nanoribbons with defects

The conductances of two typical metallic graphene nanoribbons with one and two defects are studied using the tight binding model with the surface Green’s function method. The weak scattering impurities, U ～ 1 eV, induce a dip in the conductance near the Fermi energy for the narrow zigzag graphene nanoribbons. As the impurity scattering strength increases, the conductance behavior at the Fermi energy becomes more complicated and depends on the impurity location, the AA and AB sites. The impurity effect then becomes weak and vanishes with the increase in the width of the zigzag graphene nanoribbons (150 nm). For the narrow armchair graphene nanoribbons, the conductance at the Fermi energy is suppressed by the impurities and becomes zero with the increase in impurity scattering strength, U > 100 eV, for two impurities at the AA sites, but becomes constant for the two impurities at the AB sites. As the width of the graphene nanoribbons increases, the impurity effect on the conductance at the Fermi energy depends sensitively on the vacancy location at the AA or AB sites.     

Anisotropic Short-Wavelength Friedel Oscillation with Adjustable Envelope in Graphene

We investigate theoretically the intervalley charge density oscillation and the screened ionic potential in graphene caused by the intervalley scattering. We demonstrate that the contribution from the intervalley scattering is comparable with that from the intravalley scattering, and oscillation rather than decaying dominates at a large distance away from the external impurity. We show that the intervalley oscillation is strongly anisotropic because of the inequivalency between neighboring valleys. The anisotropic oscillation consists of an anisotropic short-wavelength oscillation with an anisotropic fixed wavelength and an isotropic long-wavelength envelop with an isotropic wavelength modulated by doping, making an adjustable-widthed wave-packet propagation. One weakens the screening and gets anisotropic short-wavelength oscillation by introducing short-range mechanism in graphene and graphene-like materials.     

Anisotropic Short-Wavelength Friedel Oscillation with Adjustable Envelope in Graphene

We investigate theoretically the intervalley charge density oscillation and the screened ionic potential in graphene caused by the intervalley scattering. We demonstrate that the contribution from the intervalley scattering is comparable with that from the intravalley scattering, and oscillation rather than decaying dominates at a large distance away from the external impurity. We show that the intervalley oscillation is strongly anisotropic because of the inequivalency between neighboring valleys. The anisotropic oscillation consists of an anisotropic short-wavelength oscillation with an anisotropic fixed wavelength and an isotropic long-wavelength envelop with an isotropic wavelength modulated by doping, making an adjustable-widthed wave-packet propagation. One weakens the screening and gets anisotropic short-wavelength oscillation by introducing short-range mechanism in graphene and graphene-like materials.     

Effect of charged impurity correlations on transport in monolayer and bilayer graphene

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 higher carrier densities. We show that in the presence of correlation among charged impurities the conductivity depends nonlinearly on the impurity density n_i and can increase with n_i.     

Final-state effects in the excitation spectra of deep impurities in semiconductors

The excitation spectra of deep impurities have usually been interpreted in terms of transitions to continuum states having the same energy distribution and Bloch-like character as the perfect-crystal band states. Here we provide theoretical analysis and experimental evidence showing that deep-level spectra may in fact be dominated by bound and quasibound final states induced by the strong short-range impurity potentials.     

Measurement of scattering rate and minimum conductivity in graphene

The conductivity of graphene samples with various levels of disorder is investigated for a set of specimens with mobility in the range of 1-20x10(3) cm2/V sec. Comparing the experimental data with the theoretical transport calculations based on charged impurity scattering, we estimate that the impurity concentration in the samples varies from 2-15x10(11) cm(-2). In the low carrier density limit, the conductivity exhibits values in the range of 2-12e2/h, which can be related to the residual density induced by the inhomogeneous charge distribution in the samples. The shape of the conductivity curves indicates that high mobility samples contain some short-range disorder whereas low mobility samples are dominated by long-range scatterers.     

Temperature-dependent subband mobility characteristics in n-doped silicon junctionless nanowire transistor

We have investigated the temperature-dependent effective mobility characteristics in impurity band and conduction subbands of n-doped silicon junctionless nanowire transistors. It is found that the electron effective mobility of the first subband in 2-fold valleys is higher than that of the second subband in 4-fold valleys. There exists a maximum value for the effective subband mobilities at low temperatures, which is attributed to the increase of thermally activated electrons from the ionized donors in the impurity band. The experimental results indicate that the effective subband mobility is temperature-dependent on the electron interactions by thermal activation, impurity scattering, and intersubband scattering.     

Metal-to-insulator transition and electron-hole puddle formation in disordered graphene nanoribbons

The experimentally observed metal-to-insulator transition in hydrogenated graphene is numerically confirmed for actual sized graphene samples and realistic impurity concentrations. The eigenstates of our tight-binding model with substitutional disorder corroborate the formation of electron-hole?puddles with characteristic length scales comparable to the ones found in experiments. The puddles cause charge inhomogeneities and tend to suppress Anderson localization. Even though, monitoring the charge carrier quantum dynamics and performing a finite-size scaling of the local density of states distribution, we find strong evidence for the existence of localized states in graphene nanoribbons with short-range but also correlated long-range disorder.     

Adatoms in graphene

We review the problem of adatoms in graphene under two complementary points of view, scattering theory and strong correlations. We show that in both cases impurity atoms on the graphene surface present effects that are absent in the physics of impurities in ordinary metals. We discuss how to observe these unusual effects with standard experimental probes such as scanning tunneling microscopes, and spin susceptibility.     

The influence of impurity formation on electron inelastic scattering of suspended graphene

This study reports on controlling the formation of nanoimpurities on suspended graphene to investigate the inelastic scattering of electrons using a two‐phonon Raman process. Results were analyzed by transmission electron microscopy (TEM) and scanning Raman spectroscopy in the same region of suspended graphene. The findings revealed that the area with a higher concentration of impurities shown in the TEM image corresponds directly to the area with a lower integrated intensity and a wider full width at half maximum in the Raman mapping of the 2D band and vice versa. The same trend is also apparent in the 2D′ and D + D″ bands. In conclusion, the results are explained by an increase in the electronic scattering rate due to impurities, which affects two‐phonon Raman scattering. Combining the TEM image and Raman mapping image effectively demonstrates how electron behavior is affected by the distribution of impurities in graphene systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Spin polarization of the current in a correlated one-dimensional conductor with an impurity

The spin transport as the current flows through an impurity in a one-dimensional conductor is analyzed. The interacting electrons are described in terms of the Luttinger liquid theory. Both the Coulomb and short-range interactions are considered; the latter appears when the gate screens the long-range part of the Coulomb potential. The cases of magnetic and nonmagnetic impurities are considered. It has been revealed that, for a magnetic impurity, the electric current flow induces the generation of the spin current, which has direct and alternating components. At low temperatures and voltages, the current can be completely spin-polarized. For a nonmagnetic impurity, the spin current generation is absent. The spin current flowing though the wire affects the current-voltage characteristic for both magnetic and nonmagnetic impurities. The results have been obtained for a rather strong electron-electron interaction.     

Graphene valley filter using a line defect

With its two degenerate valleys at the Fermi level, the band structure of graphene provides the opportunity to develop unconventional electronic applications. Herein, we show that electron and hole quasiparticles in graphene can be filtered according to which valley they occupy without the need to introduce confinement. The proposed valley filter is based on scattering off a recently observed line defect in graphene. Quantum transport calculations show that the line defect is semitransparent and that quasiparticles arriving at the line defect with a high angle of incidence are transmitted with a valley polarization near 100%.     

Indirect magnetic exchange interaction mediated by bound Landau states in 2DES

The possibility of indirect exchange coupling mediated by Landau electrons bound to magnetic impurities in 2DES is studied here. The importance of the resonance scattering of the Landau electrons with the impurities is emphasized due to its spin selectivity which results in strong spin polarization of the localized Landau states. The bound Landau states act as mediators of the superexchange interaction resulting in an antiferromagnetic interaction between the nuclear spins of the impurities. The coupling constant, between these nuclear spins, J, is presented for the case of a weak scattering limit and found to depend strongly on the ratio of the impurity separation over the magnetic length. Possible applications of these results may include a long-range mechanism for coupling between two nuclear spins to be used as a qubits interaction with a spacing distance of the order of the magnetic length.     

Propagation of states in dilation analytic potentials and asymptotic completeness

We estimate the space-time behavior of scattering states for two-body Schrödinger operators with smooth, dilation analytic potentials. We use our estimates to give a simple proof of asymptotic completeness for a class of long-range potentials, including the Coulomb potential plus a fairly general short-range perturbation.Supported by USNSF Grant MCS-78-01885     

Diffusion of electrons scattered by short-range impurities in a quantizing magnetic field

Formulas for transverse diffusion and conductivity in a semiconductor are obtained for electrons scattered by neutral impurities in a quantizing magnetic field. The formulas are valid for an impurity potential of arbitrary depth. Based on Kubo’s theory [1], calculations are performed using electron wavefunctions of the problem of single-impurity scattering in a magnetic field [2]. The poles of the scattering amplitude correctly determine electron eigenstates and magnetic impurity states. As a result, an exact expression is found for the dependence of transverse diffusion coefficient D _⊥ on longitudinal electron energy ? due to scattering by short-range (neutral) impurities. The behavior of D _⊥(?) is examined over an interval of magnetic field strength for several values of impurity potential depth. The experimental observability of diffusion and conductivity using IR lasers is discussed.     

Electronic Raman Scattering in Graphene

Linear dispersion near the Dirac points in the band structure of graphenes can give rise to novel physical properties. We calculate the electronic contribution to the Raman spectra in graphenes, which also shows novel features. In the clean limit, the Raman spectrum in the undoped graphene is linear （with a universal slope against impurity scattering） at low energy due to the linear dispersion near the Dirae points, and it peaks at a position corresponding to the van Hove singularity in the band structure. In a doped graphene, the electronic Raman absorption is forbidden up to a vertical inter-band particle-hole gap. Beyond the gap the spectrum follows the undoped case. In the presence of impurities, absorption within the gap （in the otherwise clean case） is induced, which is identified as the intra-band contribution. The Drude-like intra-band contribution is seen to be comparable to the higher energy inter-band Raman peak. The results are discussed in connection to experiments.     

Charge asymmetry and neutron-neutron scattering

The uncertainty in the subtraction of electromagnetic effects from S-wave proton-proton scattering potentials is studied in two models using unitarily transformed potentials. Restrictions on these models caused by theoretical, off-shell and deuteron constraints are imposed. The probable uncertainty of physical interest is found to be small. It is typically only a few parts per thousand of the one-pion exchange potential. It has relatively little effect on Coulomb displacement energies. Phenomenological charge-symmetry-breaking potentials are constructed which both fit the experimental neutron-neutron (nn) scattering length (?16.4 fm). and give roughly the needed Coulomb displacement energies. These phenomenological potentials are found to contain a short-range repulsion and a strong long-range attraction for a neutron pair. The need for experimental information on the shape and state dependence of the nn force is emphasized. These can probably be obtained from precise nn scattering measurements.     

Skew scattering of the electrons by Ce impurities in La

Low temperature measurements of the Hall effect in lanthanum containing cerium impurities show, in addition to the ordinary Hall effect, a contribution (nearly) proportional to the magnetization of the cerium magnetic moments. We ascribe this contribution to skew scattering by the cerium impurities. The asymmetry of the scattering can result from the mixing of the conduction band and impurity wave functions for impurities having orbital magnetism.