Charge transport in graphene with resonant scatterers

Imaging resonant dissipation from individual atomic defects in graphene

Conversion of electric current into heat involves microscopic processes that operate on nanometer length scales and release minute amounts of power. Although central to our understanding of the electrical properties of materials, individual mediators of energy dissipation have so far eluded direct observation. Using scanning nanothermometry with submicrokelvin sensitivity, we visualized and controlled phonon emission from individual atomic-scale defects in graphene. The inferred electron-phonon "cooling power spectrum" exhibits sharp peaks when the Fermi level comes into resonance with electronic quasi-bound states at such defects. Rare in the bulk but abundant at graphene's edges, switchable atomic-scale phonon emitters provide the dominant dissipation mechanism. Our work offers insights for addressing key materials challenges in modern electronics and enables control of dissipation at the nanoscale.

Flat-Lens Focusing of Electron Beams in Graphene

Coupling electron beams carrying information into electronic units is fundamental in microelectronics. This requires precision manipulation of electron beams through a coupler with a good focusing ability. In graphene, the focusing of wide electron beams has been successfully demonstrated by a circular p-n junction. However, it is not favorable for information coupling since the focal length is so small that the focal spot locates inside the circular gated region, rather than in the background region. Here, we demonstrate that an array of gate-defined quantum dots, which has gradually changing lattice spacing in the direction transverse to propagation, can focus electrons outside itself, providing a possibility to make a coupler in graphene. The focusing effect can be understood as due to the gradient change of effective refractive indices, which are defined by the local energy band in a periodic potential. The strong focusing can be achieved by suitably choosing the lattice gradient and the layer number in the incident direction, offering an effective solution to precision manipulation of electron beams with wide electron energy range and high angular tolerance.

Lévy Flights due to Anisotropic Disorder in Graphene

We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed backscattering are formed in this model in the direction of the lines. The system reveals Lévy-flight transport in the stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities, which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent T-matrix approximation.

Scattering strength of the scatterer inducing variability in graphene on silicon oxide

Large variability of carrier mobility of graphene-based field effect transistors hampers graphene science and technology. We show that the number of the scatterer responsible for the observed variability on graphene devices on silicon oxide can be determined by finding the number of hydrogen that can be chemisorbed on graphene. We use the relationship between the number of the scatterer and the mobility of graphene devices to determine that the variability-inducing scatterer possesses scattering strength 10 times smaller than that of adsorbed potassium atoms and 50 times smaller than that of ion-beam induced vacancies. Our results provide an important, quantitative input towards determining the origin of the variability.

Suppressing Klein tunneling in graphene using a one-dimensional array of localized scatterers

Graphene's unique physical and chemical properties make it an attractive platform for use in micro- and nanoelectronic devices. However, electrostatically controlling the flow of electrons in graphene can be challenging as a result of Klein tunneling, where electrons normally incident to a one-dimensional potential barrier of height V are perfectly transmitted even as V → ∞. In this study, theoretical and numerical calculations predict that the transmission probability for an electron wave normally incident to a one-dimensional array of localized scatterers can be significantly less than unity when the electron wavelength is smaller than the spacing between scatterers. In effect, placing periodic openings throughout a potential barrier can, somewhat counterintuitively, decrease transmission in graphene. Our results suggest that electrostatic potentials with spatial variations on the order of the electron wavelength can suppress Klein tunneling and could find applications in developing graphene electronic devices.

Density of states in a two-dimensional chiral metal with vacancies

We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with vacancies. We demonstrate that randomly distributed vacancies constitute a peculiar type of chiral disorder leading to strong modifications of critical properties at zero energy as compared to those of conventional chiral metals. In particular, the average density of states diverges as ρ∝E(-1)|lnE|(-3/2) and the correlation length L(c)∝√[|lnE|] in the limit E→0. When the average density of vacancies is different in the two sublattices, a finite concentration of zero modes emerges and a gap in the quasiclassical density of states opens around zero energy. Interference effects smear this gap, resulting in exponentially small tails at low energies.

Spin-orbit interaction and isotropic electronic transport in graphene

Broken symmetries in graphene affect the massless nature of its charge carriers. We present an analysis of scattering by defects in graphene in the presence of spin-orbit interactions (SOIs). A characteristic constant ratio (≃2) of the transport to elastic times for massless electrons signals the anisotropy of the scattering. We show that SOIs lead to a drastic decrease of this ratio, especially at low carrier concentrations, while the scattering becomes increasingly isotropic. As the strength of the SOI determines the energy (carrier concentration) where this drop is more evident, this effect could help evaluate these interactions through transport measurements in graphene systems with enhanced spin-orbit coupling.

Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point

We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity σ is equal to the ballistic value 4e2/πh for each disorder realization, provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point with σ≃4×0.4e2/h at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is also obtained at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes: remarkably, all key manifestations of Anderson localization and criticality in two dimensions are observed numerically in a single setup.

Topological aspects of charge-carrier transmission across grain boundaries in graphene

Dislocations and grain boundaries are intrinsic topological defects of large-scale polycrystalline samples of graphene. These structural irregularities have been shown to strongly affect electronic transport in this material. Here, we report a systematic investigation of the transmission of charge carriers across the grain-boundary defects in polycrystalline graphene by means of the Landauer-Büttiker formalism within the tight-binding approximation. Calculations reveal a strong suppression of transmission at low energies upon decreasing the density of dislocations with the smallest Burgers vector b = (1,0). The observed transport anomaly is explained from the point of view of resonant backscattering due to localized states of topological origin. These states are related to the gauge field associated with all dislocations characterized by b = (n,m) with n - m ≠ 3q (q ∈ Z). Our work identifies an important source of charge-carrier scattering caused by the topological defects present in large-area graphene samples produced by chemical vapor deposition.

Structure of a peptide adsorbed on graphene and graphite

Noncovalent functionalization of graphene using peptides is a promising method for producing novel sensors with high sensitivity and selectivity. Here we perform atomic force microscopy, Raman spectroscopy, infrared spectroscopy, and molecular dynamics simulations to investigate peptide-binding behavior to graphene and graphite. We studied a dodecamer peptide identified with phage display to possess affinity for graphite. Optical spectroscopy reveals that the peptide forms secondary structures both in powder form and in an aqueous medium. The dominant structure in the powder form is α-helix, which undergoes a transition to a distorted helical structure in aqueous solution. The peptide forms a complex reticular structure upon adsorption on graphene and graphite, having a helical conformation different from α-helix due to its interaction with the surface. Our observation is consistent with our molecular dynamics calculations, and our study paves the way for rational functionalization of graphene using biomolecules with defined structures and, therefore, functionalities.

Mapping the density of scattering centers limiting the electron mean free path in graphene

Recently, giant carrier mobility μ (>10(5) cm(2) V(-1) s(-1)) and micrometer electron mean free path (l) have been measured in suspended graphene or in graphene encapsulated between inert and ultraflat BN layers. Much lower μ values (10000-20000 cm(2) V(-1) s(-1)) are typically reported in graphene on common substrates (SiO(2), SiC) used for device fabrication. The debate on the factors limiting graphene electron mean free path is still open with charged impurities (CI) and resonant scatterers (RS) indicated as the most probable candidates. As a matter of fact, the inhomogeneous distribution of such scattering sources in graphene is responsible of nanoscale lateral inhomogeneities in the electronic properties, which could affect the behavior of graphene nanodevices. Hence, high resolution two-dimensional (2D) mapping of their density is very important. Here, we used scanning capacitance microscopy/spectroscopy to obtain 2D maps of l in graphene on substrates with different dielectric permittivities, that is, SiO(2) (κ(SiO2) = 3.9), 4H-SiC (0001) (κ(SiC) = 9.7) and the very-high-κ perovskite strontium titanate, SrTiO(3) (001), briefly STO (κ(STO) = 330). After measuring l versus the gate bias V(g) on an array of points on graphene, maps of the CI density (N(CI)) have been determined by the neutrality point shift from V(g) = 0 V in each curve, whereas maps of the RS density (N(RS)) have been extracted by fitting the dependence of l on the carrier density (n). Laterally inhomogeneous densities of CI and RS have been found. The RS distribution exhibits an average value ∼3 × 10(10) cm(-2) independently on the substrate. For the first time, a clear correlation between the minima in the l map and the maxima in the N(CI) map is obtained for graphene on SiO(2) and 4H-SiC, indicating that CI are the main source of the lateral inhomogeneity of l. On the contrary, the l and N(CI) maps are uncorrelated in graphene on STO, while a clear correlation is found between l and N(RS) maps. This demonstrates a very efficient dielectric screening of CI in graphene on STO and the role of RS as limiting factor for electron mean free path.

Magnetoresistance and magnetic ordering fingerprints in hydrogenated graphene

Spin-dependent features in the conductivity of graphene, chemically modified by a random distribution of hydrogen adatoms, are explored theoretically. The spin effects are taken into account using a mean-field self-consistent Hubbard model derived from first-principles calculations. A Kubo transport methodology is used to compute the spin-dependent transport fingerprints of weakly hydrogenated graphene-based systems with realistic sizes. Conductivity responses are obtained for paramagnetic, antiferromagnetic, or ferromagnetic macroscopic states, constructed from the mean-field solutions obtained for small graphene supercells. Magnetoresistance signals up to ∼7% are calculated for hydrogen densities around 0.25%. These theoretical results could serve as guidance for experimental observation of induced magnetism in graphene.

Color-dependent conductance of graphene with adatoms

We study ballistic transport properties of graphene with a low concentration of vacancies or adatoms. The conductance of graphene doped to the Dirac point is found to depend on the relative distribution of impurities among different sites of the honeycomb lattice labeled in general by six colors. The conductivity is shown to be sensitive to the crystal orientation if adatom sites have a preferred color. Our theory is confirmed by numerical simulations using recursive Green's functions with no adjustable parameters.

Diffusion and criticality in undoped graphene with resonant scatterers

A general theory is developed to describe graphene with an arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the Dirac-point conductivity σ of graphene with resonant scatterers. In the case of smooth resonant impurities the symmetry class is identified as DIII and σ grows logarithmically with increasing impurity concentration. For vacancies (or strong on-site potential impurities, class BDI) σ saturates at a constant value that depends on the vacancy distribution among two sublattices.

On resonant scatterers as a factor limiting carrier mobility in graphene

We show that graphene deposited on a substrate has a non-negligible density of atomic scale defects. This is evidenced by a previously unnoticed D peak in the Raman spectra with intensity of ∼1% with respect to the G peak. We evaluated the effect of such impurities on electron transport by mimicking them with hydrogen adsorbates and measuring the induced changes in both mobility and Raman intensity. If the intervalley scatterers responsible for the D peak are monovalent, their concentration is sufficient to account for the limited mobilities currently achievable in graphene on a substrate.

Resonant scattering by realistic impurities in graphene

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 adatoms such as H absorbed to graphene are shown to create midgap states within ±0.03  eV 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 contaminated with these realistic impurities in accordance with recent experiments.

Disorder and electronic transport in graphene

In this review, we provide an account of the recent progress in understanding electronic transport in disordered graphene systems. Starting from a theoretical description that emphasizes the role played by band structure properties and lattice symmetries, we describe the nature of disorder in these systems and its relation to transport properties. While the focus is primarily on theoretical and conceptual aspects, connections to experiments are also included. Issues such as short- versus long-range disorder, localization (strong and weak), the carrier density dependence of the conductivity, and conductance fluctuations are considered and some open problems are pointed out.