The influence of plasma etched sample edges on electrical transport and doping is studied. Through electrical transport measurements the overall doping and mobility are analyzed for mono- and bilayer graphene samples. As a result the edge contributes strongly to the overall doping of the samples. Furthermore the edge disorder can be found as the main limiting source of the mobility for narrow samples.
We consider two mechanisms of spin relaxation in disordered graphene. i) Spin relaxation due to curvature spin orbit coupling caused by ripples. ii) Spin relaxation due to the interaction of the electronic spin with localized magnetic moments at the edges. We obtain analytical expressions for the spin relaxation times, tau_SO and tau_J due to both mechanisms and estimate their values for realistic parameters of graphene samples. We obtain that spin relaxation originating from these mechanisms is very weak and spin coherence is expected in disordered graphene up to samples of length L ~ 1 micro…
Graphene nanoribbons provide an opportunity to integrate phase-coherent transport phenomena with nanoelectromechanical systems (NEMS). Due to the strain induced by a deflection in a graphene nanoribbon resonator, coherent electron transport and mechanical deformations couple. As the electrons in graphene have a Fermi wavelength λ~ a_0 = 1.4 Å, this coupling can be used for sensitive displacement detection in both armchair and zigzag graphene nanoribbon NEMS. Here it is shown that for ordered as well as disordered ribbon systems of length L, a strain ε~ (w/L)^2 due to a deflection w leads to a …
We have observed the quantum Hall effect (QHE) and Shubnikov-de Haas (SdH) oscillations in highly disordered graphene at magnetic fields up to 65 T. Disorder was introduced by hydrogenation of graphene up to a ratio H/C $\approx 0.1\%$. The analysis of SdH oscillations and QHE indicates that the topological part of the Berry phase, proportional to the pseudo-spin winding number, is robust against introduction of disorder by hydrogenation in large scale graphene.
Using the partition-free time-dependent Landauer-B{ü}ttiker formalism for transient current correlations, we study the traversal times taken for electrons to cross graphene nanoribbon (GNR) molecular junctions. We demonstrate electron traversal signatures that vary with disorder and orientation of the GNR. These findings can be related to operational frequencies of GNR-based devices and their consequent rational design.
An accurate simulation of Green's function and self-energy function of non-interacting electrons in disordered graphenes are performed. Fundamental physical quantities such as the elastic relaxation time τe, the phase velocity vp, and the group velocity vg are evaluated. New features around the Dirac point are revealed, showing hints that multi-scattering induced hybridization of Bloch states plays an important role in the vicinity of the Dirac point.
We measured the conductance fluctuation of bi- and trilayer graphene devices prepared on mechanical exfoliated graphene by an all-dry, lithography-free process using an ultrathin quartz filament as a shadow mask. Reproducible fluctuations in conductance as a function of applied gate voltage or magnetic field were found. As the gate voltage was tuned so that the graphene device was pushed to the charge neutral point, the amplitude of the conductance fluctuation was found to be suppressed quickly from a value consistent with universal conductance fluctuation when the devices were still well with…
An analytic theory of electron transport in disordered graphene in a ballistic geometry is developed. We consider a sample of a large width W and analyze the evolution of the conductance, the shot noise, and the full statistics of the charge transfer with increasing length L, both at the Dirac point and at a finite gate voltage. The transfer matrix approach combined with the disorder perturbation theory and the renormalization group is used. We also discuss the crossover to the diffusive regime and construct a ``phase diagram'' of various transport regimes in graphene.
At low values of external doping graphene displays a wealth of unconventional transport properties. Perhaps most strikingly, it supports a robust 'metallic' regime, with universal conductance of the order of the conductance quantum. We here apply a combination of mean field and bosonization methods to explore the large scale transport properties of the system. We find that, irrespective of the doping level, disordered graphene is subject to common mechanisms of Anderson localization. However, at low doping a number of renormalization mechanisms conspire to protect the conductivity of the syste…
The law of reflection states that smooth surfaces reflect waves specularly, thereby acting as a mirror. This law is insensitive to disorder as long as its length scale is smaller than the wavelength. Monolayer graphene exhibits a linear dispersion at low energies and consequently a diverging Fermi wavelength. We present proof that for a disordered graphene boundary, resonant scattering off disordered edge modes results in diffusive electron reflection even when the electron wavelength is much longer than the disorder correlation length. Using numerical quantum transport simulations, we demonst…
The full counting statistics of the charge transport through an undoped graphene sheet in the presence of smooth disorder is studied. At the Dirac point both in clean and diffusive limits, transport properties of a graphene sample are described by the universal Dorokhov distribution of transmission probabilities. In the crossover regime, deviations from universality occur which can be studied analytically both on ballistic and diffusive sides. In the ballistic regime, we use a diagrammatic technique with matrix Green functions. For a diffusive system, the sigma model is applied. Our results ar…
Random fluctuations of the shot-noise power in disordered graphene nanoribbons are studied. In particular, we calculate the distribution of the shot noise of nanoribbons with zigzag and armchair edge terminations. We show that the shot noise statistics is different for each type of these two graphene structures, which is a consequence of presence of different electron localizations: while in zigzag nanoribbons electronic edge states are Anderson localized, in armchair nanoribbons edge states are absent, but electrons are anomalously localized. Our analytical results are verified by tight bindi…
We study the effect of disordered ripples on the conductivity of monolayer graphene flakes. We calculate the relaxation times and the Boltzmann conductivities associated with two mechanisms. First, we study the conductivity correction due to an external in-plane magnetic field $B_\parallel$. Due to the irregular local curvature found at graphene sheets deposited over a substrate, $B_\parallel$ can be mapped into an effective random magnetic field perpendicular to the graphene surface. Second, we study the electron momentum relaxation due to intrinsic pseudo magnetic fields originated from defo…
We study numerically the effects of edge and bulk disorder on the conductance of graphene nanoribbons. We compute the conductance suppression due to localization induced by edge scattering. We find that even for weak edge roughness, conductance steps are suppressed and transport gaps appear. These gaps are approximately inversely proportional to the nanoribbon width. On/off conductance ratios grow exponentially with the nanoribbon length. Our results impose severe limitations to the use of graphene in ballistic nanowires.
We present numerical studies of conduction in graphene nanoribbons with different types of disorder. We find that even when defect scattering depresses the conductance to values two orders of magnitude lower than 2e^2/h, equally spaced conductance plateaus occur at moderately low temperatures due to enhanced electron backscattering near subband edge energies if bulk vacancies are present in the ribbon. This work accounts quantitatively for the surprising conductance quantization observed by Lin et al. [Phys. Rev. B 78, 161409 (2008)] in ribbons with such low conductances.
A tight-binding model with randomly fluctuating atomic positions is studied to discuss the effect of strong disorder in graphene. We employ a strong-disorder expansion for the transport quantities and find a diffusive behavior, where the conductivity is decreasing with increasing disorder. Surprisingly, the magnetic field drops out of the transport quantities in leading order of this expansion. This signals a strong suppression of magnetotransport effects for sufficiently strong disorder. This result is consistent with recent experimental observations by Morozov {\it et al.}
We present transport measurements on quantum dots of sizes 45, 60 and 80 nm etched with an Ar/O2-plasma into a single graphene sheet, allowing a size comparison avoiding effects from different graphene flakes. The transport gaps and addition energies increase with decreasing dot size, as expected, and display a strong correlation, suggesting the same physical origin for both, i.e. disorder-induced localization in presence of a small confinement gap. Gate capacitance measurements indicate that the dot charges are located in the narrow device region as intended. A dominant role of disorder is fu…
We show a dramatic deviation from ergodicity for the conductance fluctuations in graphene. In marked contrast to the ergodicity of dirty metals, fluctuations generated by varying magnetic field are shown to be much smaller than those obtained when sweeping Fermi energy. They also exhibit a strongly anisotropic response to the symmetry-breaking effects of a magnetic field, when applied perpendicular or parallel to the graphene plane. These results reveal a complex picture of quantum interference in graphene, whose description appears more challenging than for conventional mesoscopic systems.
We present a magneto-transport study of graphene samples into which a mild disorder was introduced by exposure to ozone. Unlike the conductivity of pristine graphene, the conductivity of graphene samples exposed to ozone becomes very sensitive to temperature: it decreases by more than 3 orders of magnitude between 100K and 1K. By varying either an external gate voltage or temperature, we continuously tune the transport properties from the weak to the strong localization regime. We show that the transition occurs as the phase coherence length becomes comparable to the localization length. We al…
We report on (magneto)-transport experiments in chemically derived narrow graphene nanoribbons under high magnetic fields (up to 60 Tesla). Evidences of field-dependent electronic confinement features are given, and allow estimating the possible ribbon edge symmetry. Besides, the measured large positive magnetoconductance indicates a strong suppression of backscattering induced by the magnetic field. Such scenario is supported by quantum simulations which consider different types of underlying disorders (smooth edge disorder and long range Coulomb scatters).
Using the recursive Green's function method, we study the problem of electron transport in a disordered single-layer graphene sheet. The conductivity is of order $e^2/h$ and its dependence on the carrier density has a scaling form that is controlled solely by the disorder strength and the ratio between the sample size and the correlation length of the disorder potential. The shot noise Fano factor is shown to have a narrow dip near the neutrality point for weak disorder and to develop a nearly doping independent behavior at strong disorder. Our results are in good qualitative and quantitative …
We report an electron transport study of lithographically fabricated graphene nanoribbons of various widths and lengths at different temperatures. At the charge neutrality point, a length-independent transport gap forms whose size is inversely proportional to the width. In this gap, electron is localized, and charge transport exhibits a transition between simple thermally activated behavior at higher temperatures and a variable range hopping at lower temperatures. By varying the geometric capacitance through the addition of top gates, we find that charging effects constitute a significant port…
The orbital magnetism is studied in graphene monolayer within the effective mass approximation. In models of short-range and long-range disorder, the magnetization is calculated with self-consistent Born approximation. In the zero-field limit, the susceptibility becomes highly diamagnetic around zero energy, while it has a long tail proportional to the inverse of the Fermi energy. We demonstrated how the magnetic oscillation vanishes and converges to the susceptibility, on going from a strong-field regime to zero-field. The behavior at zero energy is shown to be highly singular.
Experiments on hexagonal graphene-like structures using microwave measuring techniques are presented. The lowest transverse-electric resonance of coupled dielectric disks sandwiched between two metallic plates establishes a tight-binding configuration. The nearest-neighbor coupling approximation is investigated in systems with few disks. Taking advantage of the high flexibility of the disks positions, consequences of the disorder introduced in the graphene lattice on the Dirac points are investigated. Using two different types of disks, a boron-nitride-like structure (a hexagonal lattice with …
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…
We report on magneto-transport measurement in disordered graphene under pulsed magnetic field of up to 57T. For large electron or hole doping, the system displays the expected anomalous Integer Quantum Hall Effect (IQHE) specific to graphene up to filling factor $ν=2$. In the close vicinity of the charge neutrality point, the system breaks up into co-existing puddles of holes and electrons, leading to a vanishing Hall and finite longitudinal resistance with no hint of divergence at very high magnetic field. Large resistance fluctuations are observed near the Dirac point. They are interpreted a…
The inhomogenous real-space electronic structure of gapless and gapped disordered bilayer graphene is calculated in the presence of quenched charge impurities. For gapped bilayer graphene we find that for current experimental conditions the amplitude of the fluctuations of the screened disorder potential is of the order of (or often larger than) the intrinsic gap $Δ$ induced by the application of a perpendicular electric field. We calculate the crossover chemical potential, $Δ_{\rm cr}$, separating the insulating regime from a percolative regime in which less than half of the area of the bilay…
Conductance fluctuations produced by the presence of disorder in zigzag and armchair graphene nanoribbons are studied. We show that quantum transport in zigzag nanoribbons takes place via edge states which are exponentially localized, as in the standard Anderson localization problem, whereas for armchair nanoribbons the symmetry of the graphene sublattices produces anomalous localization, or delocalization. We show that these two different electron localizations lead to significant differences of the conductance statistics between zigzag and armchair nanoribbons. In particular, armchair nanori…
We report anomalous quantum transport features in bilayer graphene in presence of a random distribution of structural vacancies. By using an efficient real-space Kubo-Greenwood transport methodology, the impact of a varying density of dimer versus non-dimer vacancies is investigated in very large scale disordered models. While non-dimer vacancies are shown to induce localization regimes, dimer vacancies result in an unexpected ballistic regime whose energy window surprisingly enlarges with increasing impurity density. Such counterintuitive phenomenon is explained by the formation of an effecti…
We report a theoretical low-field magnetotransport study unveiling the effect of pseudospin in realistic models of weakly disordered graphene-based materials. Using an efficient Kubo computational method, and simulating the effect of charges trapped in the oxide, different magnetoconductance fingerprints are numerically obtained in system sizes as large as 0.3 micronmeter squared, containing tens of millions of carbon atoms. In two-dimensional graphene, a strong valley mixing is found to irreparably yield a positive magnetoconductance (weak localization), whereas crossovers from positive to a …
We have studied the transport properties of a large graphene double quantum dot under the influence of background disorder potential and magnetic field. At low temperatures, the evolution of the charge-stability diagram as a function of B-field is investigated up to 10 Tesla. Our results indicate that the charging energy of quantum dot is reduced, and hence the size of the dot increases, at high magnetic field. We provide an explanation of our results using a tight-binding model, which describes the charge redistribution in a disordered graphene quantum dot via the formation of Landau levels a…
In this paper, the average density of states (ADOS) with a binary alloy disorder in disordered graphene systems are calculated based on the recursion method. We observe an obvious resonant peak caused by interactions with surrounding impurities and an anti-resonance dip in ADOS curves near the Dirac point. We also find that the resonance energy (Er) and the dip position are sensitive to the concentration of disorders (x) and their on-site potentials (v). An linear relation, not only holds when the impurity concentration is low but this relation can be further extended to high impurity concentr…
We analyze numerically ensembles of tight-binding Hamiltonians describing highly-symmetric graphene nanoflakes with weak diagonal disorder induced by random electrostatic potential landscapes. When increasing the disorder strength, statistical distribution of energy levels evolves from Poissonian to Wigner, indicating the transition to quantum chaos. Power laws with the universal exponent map the disorder strength in nanoflakes of different sizes, boundaries, and microscopic disorder types onto a single parameter in additive random-matrix model.
The role of defect-induced zero-energy modes on charge transport in graphene is investigated using Kubo and Landauer transport calculations. By tuning the density of random distributions of monovacancies either equally populating the two sublattices or exclusively located on a single sublattice, all conduction regimes are covered from direct tunneling through evanescent modes to mesoscopic transport in bulk disordered graphene. Depending on the transport measurement geometry, defect density, and broken sublattice-symmetry, the Dirac point conductivity is either exceptionally robust against dis…
We report and analyze low-temperature measurements of the conductance of partially disordered reduced graphene oxide, finding that the data follow a simple crossover scenario. At room temperature, conductance is dominated by two-dimensional (2D) electric field-assisted, thermally-driven (Pollak-Riess) variable-range hopping (VRH) through highly-disordered regions. However, at lower temperatures T, we find a smooth crossover to follow the exp(-E_0/E)^(1/3) field-driven (Shklovskii) 2D VRH conductance behaviour when the electric field E exceeds a specific crossover value E_C (T)_2D = (E_a E_0^(1…
We calculate the electronic and thermal transport properties of devices based on finite graphene antidot lattices (GALs) connected to perfect graphene leads. We use an atomistic approach based on the $π$-tight-binding model, the Brenner potential, and employing recursive Green's functions. We consider the effect of random disorder on the electronic and thermal transport properties, and examine the potential gain of thermoelectric merit by tailoring of the disorder. We propose several routes to optimize the transport properties of the GAL systems. Finally, we illustrate how quantum thermal tran…
We calculate the average single particle density of states in graphene with disorder due to impurity potentials. For unscreened short-ranged impurities, we use the non-self-consistent and self-consistent Born and $T$-matrix approximations to obtain the self-energy. Among these, only the self-consistent $T$-matrix approximation gives a non-zero density of states at the Dirac point. The density of states at the Dirac point is non-analytic in the impurity potential. For screened short-ranged and charged long-range impurity potentials, the density of states near the Dirac point typically increases…
Raman scattering (RS) spectra and current-voltage characteristics at room temperature were measured in six series of small samples fabricated by means of electron-beam lithography on the surface of a large size (5x5 mm) industrial monolayer graphene film. Samples were irradiated by different doses of C${}^+$ ion beam up to $10^{15}$ cm${}^{-2}$. It was observed that at the utmost degree of disorder, the Raman spectra lines disappear which is accompanied by the exponential increase of resistance and change in the current-voltage characteristics.These effects are explained by suggestion that hig…
The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the di…
We have studied numerically the mesoscopic fluctuations of the conductance of a graphene strip (width W large compared to length L), in an ensemble of samples with different realizations of the random electrostatic potential landscape. For strong disorder (potential fluctuations comparable to the hopping energy), the variance of the conductance approaches the value predicted by the Altshuler-Lee-Stone theory of universal conductance fluctuations. For weaker disorder the variance is greatly enhanced if the potential is smooth on the scale of the atomic separation. There is no enhancement if the…
A non-local Hall bar geometry is used to detect neutral-current Hall effects in graphene on silicon dioxide. Disorder is tuned by the addition of Au or Ir adatoms in ultra-high vacuum. A reproducible neutral-current Hall effect is found in both as-fabricated and adatom-decorated graphene. The Hall angle exhibits a complex but reproducible dependence on gate voltage and disorder, and notably breaks electron-hole symmetry. An exponential dependence on length between Hall and inverse-Hall probes indicates a neutral current relaxation length of approximately 300 nm. The short relaxation length and…
We study the spin relaxation in graphene due to magnetic moments induced by defects. We propose and employ in our studies a microscopic model that describes magnetic impurity scattering processes mediated by charge puddles. This model incorporates the spin texture related to the defect-induced state. We calibrate our model parameters using experimentally-inferred values. The results we obtain for the spin relaxation times are in very good agreement with experimental findings. Our study leads to a comprehensive explanation for the short spin relaxation times reported in the experimental literat…
We study the localization properties of the wavefunctions in graphene flakes with short range disorder, via the numerical calculation of the Inverse Participation Ratio($IPR$) and it scaling which provides the fractal dimension $D_{2}$. We show that the edge states which exist at the Dirac point of ballistic graphene (no disorder) with zig-zag edges survive in the presence of weak disorder with wavefunctions localized at the boundaries of the flakes. We argue, that there is a strong interplay between the underlying destructive interference mechanism of the honeycomb lattice of graphene leading…
Graphene clusters consisting of 24 to 150 carbon atoms and hydrogen termination at the zigzag boundary edges have been studied, as well as clusters disordered by vacancy(s). Density Function Theory and Gaussian03 software were used to calculate graphene relative stability, desorption energy, band gap, density of states, surface shape, dipole momentum and electrical polarization of all clusters by applying the hybrid exchange-correlation functional Beke-Lee-Yang-Parr. Furthermore, infrared frequencies were calculated for two of them. Different basis sets, 6-31g**, 6-31g* and 6-31g, depending on…
The Green functions play a big role in the calculation of the local density of states of the carbon nanostructures. We investigate their nature for the variously oriented and disclinated graphene-like surface. Next, we investigate the case of a small perturbation generated by two heptagonal defects and from the character of the local density of states in the border sites of these defects we derive their minimal and maximal distance on the perturbed cylindrical surface. For this purpose, we transform the given surface into a chain using the Haydock recursion method. We will suppose only the nea…
In two dimensions chaotic level-statistics is expected for massless Dirac fermions in the presence of disorder. For weakly disordered graphene flakes with zigzag edges the obtained level-spacing distribution in the Dirac region is neither chaotic (Wigner) nor localized (Poisson) but similar to that at the critical point of the Anderson metal-insulator transition. The quantum transport in finite graphene can occur via critical edge states as in topological insulators, for strong disorder the Dirac region vanishes and graphene behaves as ordinary Anderson insulator.
Perturbations of the two dimensional carbon lattice of graphene, such as grain boundaries, have significant influence on the charge transport and mechanical properties of this material. Scanning tunneling microscopy measurements presented here show that localized states near the Dirac point dominate the local density of states of grain boundaries in graphene grown by chemical vapor deposition. Such low energy states are not reproduced by theoretical models which treat the grain boundaries as periodic dislocation-cores composed of pentagonal-heptagonal carbon rings. Using ab initio calculations…
We study the conductivity of disordered zigzag graphene nanoribbons in the incoherent regime by using the Boltzmann equation approach. The band structure of zigzag nanoribbons contains two energy valleys, and each valley has an excess one-way channel. The crucial point is that the numbers of conducting channels for two propagating directions are imbalanced in each valley due to the presence of an excess one-way channel. It was pointed out that as a consequence of this imbalance, a perfectly conducting channel is stabilized in the coherent regime if intervalley scattering is absent. We show tha…
Electron transport in a disordered graphene nanoribbon with zigzag edges is crucially affected by a perfectly conducting channel (PCC), which is stabilized if intervalley scattering is ignorable. In the presence of such a PCC, the dimensionless conductance g of the system decreases to the quantized value of g = 1 with increasing system length L. In the realistic case where intervalley scattering is weak but not ignorable, the PCC is gradually destabilized with increasing L, and g eventually decays to zero owing to the onset of Anderson localization. Here, we show that such destabilization of t…
We report on robust features of the longitudinal conductivity ($σ_{xx}$) of the graphene zero-energy Landau level in presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both $σ_{xx}$ and Hall $σ_{xy}$). As long as valley-degeneracy is maintained, the obtained critical conductivity $σ_{xx}\simeq 1.4 e^{2}/h$ is robust up…
The spin-dependent transport properties of armchair graphene nanoribbons in the presence of extrinsic spin-orbit coupling induced by a random distribution of Nickel adatoms is studied. By combining a recursive Green's function formalism with density functional theory, we explore the influence of ribbon length and metal adatom concentration on the conductance. At a given length, we observed a significant enhancement of the spin-flip channel around resonances and at energies right above the Fermi level. We also estimate the spin-relaxation length, finding values on the order of tens of micromete…
Statistical distribution of energy levels for Dirac fermions confined in a quantum dot is studied numerically on the examples of triangular and hexagonal graphene flakes with random electrostatic potential landscape. When increasing the disorder strength, level distribution evolves from Poissonian to Wigner, indicating the transition to quantum chaos. The unitary ensemble (with the twofold valley degeneracy) is observed for triangular flakes with zigzag or Klein edges and potential varying smoothly on the scale of atomic separation. For small number of edge defects, the unitary-to-orthogonal s…
The presence of strong disorder in graphene nanoribbons yields low-mobility diffusive transport at high charge densities, whereas a transport gap occurs at low densities. Here, we investigate the longitudinal and transverse magnetoresistance of a narrow (60 nm) nanoribbon in a six-terminal Hall bar geometry. At B= 11 T, quantum Hall plateaux appear at $σ_{xy}=\pm2e^2/h$, $\pm6e^2/h$ and $\pm10e^2/h$, for which the Landau level spacing is larger than the Landau level broadening. Interestingly, the transport gap does not disappear in the quantum Hall regime, when the zero-energy Landau level is …
We study interacting Dirac quasiparticles in disordered graphene and find that an interplay between the unscreened Coulomb interactions and pseudo-relativistic quasiparticle kinematics can be best revealed in the ballistic regime, whereas in the diffusive limit the behavior is qualitatively (albeit, not quantitatively) similar to that of the ordinary 2DEG with parabolic dispersion. We calculate the quasiparticle width and density of states that can be probed by photoemission, tunneling, and magnetization measurements.
We theoretically investigate light propagation and Anderson localization in one-dimensional disordered superlattices composed of dielectric stacks with graphene sheets in between. Disorder is introduced either on graphene material parameters ({\it e.g.} Fermi energy) or on the widths of the dielectric stacks. We derive an analytic expression for the localization length $ξ$, and compare it to numerical simulations using transfer matrix technique; a very good agreement is found. We demonstrate that the presence of graphene may strongly attenuate the anomalously delocalised Breswter modes, and is…
We investigate electron and phonon transport through edge disordered zigzag graphene nanoribbons based on the same methodological tool of nonequilibrium Green functions. We show that edge disorder dramatically reduces phonon thermal transport while being only weakly detrimental to electronic conduction. The behavior of the electronic and phononic elastic mean free paths points to the possibility of realizing an electron-crystal coexisting with a phonon-glass. The calculated thermoelectric figure of merit (ZT) values qualify zigzag graphene nanoribbons as a very promising material for thermoele…
We have investigated current-current correlations in a cross-shaped conductor made of graphene ribbons. We measured auto and cross correlations and compared them with the theoretical predictions for ideal diffusive conductors. Our data deviate from these predictions and agreement can be obtained only by adding contributions from occupation-number noise in the central region connecting the arms of the cross. Furthermore, we have determined Hanbury -- Brown and Twiss (HBT) exchange correlations in this system. Contrary to expectations for a cross-shaped diffusive system, we find finite HBT excha…
Gradual localization of charge carriers was studied in a series of micro-size samples of monolayer graphene fabricated on the common large scale film and irradiated by different doses of C$^+$ ions with energy 35 keV. Measurements of the temperature dependence of conductivity and magnetoresistance in fields up to 4 T showed that at low disorder, the samples are in the regime of weak localization and antilocalization. Further increase of disorder leads to strong localization regime, when conductivity is described by the variable-range-hopping (VRH) mechanism. A crossover from the Mott regime to…
We report on a numerical study of quantum transport in disordered two dimensional graphene and graphene nanoribbons. By using the Kubo and the Landauer approaches, transport length scales in the diffusive (mean free path, charge mobilities) and localized regimes (localization lengths) are computed, assuming a short range disorder (Anderson-type). In agreement with localization scaling theory, the electronic systems are found to undergo a conventional Anderson localization in the zero temperature limit. Localization lengths in weakly disordered ribbons are found to differ by two orders of magni…
