We develop an Effective Medium Theory to study the electrical transport properties of disordered graphene. The theory includes non-linear screening and exchange-correlation effects allowing us to consider experimentally relevant strengths of the Coulomb interaction. Assuming random Coulomb impurities, we calculate the electrical conductivity as a function of gate voltage describing quantitatively the full cross-over from the fluctuations dominated regime around the Dirac point to the large doping regime at high gate voltages. We find that the conductivity at the Dirac point is strongly affected by exchange correlation effects.
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.
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 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…
We study the conductance of disordered graphene superlattices with short-range structural correlations. The system consists of electron- and hole-doped graphenes of various thicknesses, which fluctuate randomly around their mean value. The effect of the randomness on the probability of transmission through the system of various sizes is studied. We show that in a disordered superlattice the quasiparticle that approaches the barrier interface almost perpendicularly transmits through the system. The conductivity of the finite-size system is computed and shown that the conductance vanishes when t…
We show that when graphene monolayers are disordered, the conductance exhibits a metallic-to-insulating transition, which opens the door to new electronic devices. The transition can be observed by driving the density or Fermi energy through the mobility edge. At the Dirac point the system is localized, whereas at higher densities there is a region of metallic behavior before the system becomes insulating again at higher densities. The region of metallic behavior depends on the disorder strength and eventually vanishes at high disorder. This result is quite unexpected since in square lattices,…
Employing the Kernel Polynomial method (KPM), we study the electronic properties of the graphene bilayers in the presence of diagonal disorder, within the tight-binding approximation. The KPM method enables us to calculate local density of states (LDOS) without need to exactly diagonalize the Hamiltonian. We use the geometrical averaging of the LDOS's at different lattice sites as a criterion to distinguish the localized states from extended ones. We find that bilayer graphene undergoes Anderson metal-insulator transition at a critical value of disorder strength.
We present a unified understanding of the experimentally observed minimal dc conductivity in weakly disordered graphene. Firstly, based on linear response theory, we reveal that randomness or disorder inevitably induces momentum dependent corrections to the electron self-energy function, which naturally yields a sample-dependent minimal conductivity. Taking the long-ranged Gaussian and Coulomb potentials as examples, we derive the momentum dependent self-energy function within the Born approximation, and further validate it via numerical simulations using the large-scale Lanczos algorithm. The…
The band structure of graphene ribbons with zigzag edges have two valleys well separated in momentum space, related to the two Dirac points of the graphene spectrum. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at band center. This feature gives rise to a perfectly conducting channel in the disordered system, if the impurity scattering does not connect the two valleys, i.e. for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through inter-valley scattering display ordinary localization behavior. …
We study electronic transport in graphene nanoribbons with rough edges. We first consider a model of weak disorder that corresponds to an armchair ribbon whose width randomly changes by a single unit cell size. We find that in this case, the low-temperature conductivity is governed by an effective one-dimensional hopping between segments of distinct band structure. We then provide numerical evidence and qualitative arguments that similar behavior also occurs in the limit of strong uncorrelated boundary disorder.
In this paper, we numerically study a Coulomb impurity problem for interacting Dirac fermions restricted in disordered graphene quantum dots. In the presence of randomly distributed lattice defects and spatial potential fluctuations, the response of the critical coupling constant for atomic collapse is mainly investigated by local density of states calculations within the extended mean-field Hubbard model. We find that both types of disorder cause an amplification of the critical threshold. As a result, up to thirty-four percent increase in the critical coupling constant is reported. This nume…
We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder. We show that the transport properties of the system depend strongly on the character of disorder. Away from half filling, the concentration dependence of conductivity is linear in the case of strong scatterers, in line with recent experimental observations, and logarithmic for weak scatterers. At half filling the conductivity is of the order of e^2/h if the randomness preserves one of the chiral symmetries of the clean Hamiltonian; otherwise, the conductivity is strongly affected …
We look at the magnetic field induced weak localisation peak of graphene samples with different mobilities. At very low temperatures, low mobility samples exhibit a very broad peak as a function of the magnetic field, in contrast to higher mobility samples, where the weak localisation peak is very sharp. We analyze the experimental data in the context of the localisation length, which allows us to extract, both the localisation length and the phase coherence length of the samples, regardless of their mobilities. This analysis is made possible by the observation that the localisation length und…
Graphene superlattices (GSLs), formed by subjecting a monolayer graphene sheet to a periodic potential, can be used to engineer band structures and, from there, charge transport properties, but these are sensitive to the presence of disorder. The localization behavior of massless 2D Dirac particles induced by weak disorder is studied for both scalar-potential and vector-potential GSLs, computationally as well as analytically by a weak-disorder expansion. In particular, it is investigated how the Lyapunov exponent (inverse localization length) depends on the incidence angle to a 1D GSL. Delocal…
We present a method for obtaining quantum transport properties in graphene that uniquely combines three crucial features: microscopic treatment of charge disorder, fully quantum mechanical analysis of transport, and the ability to model experimentally relevant system sizes. As a pertinent application we study the disorder dependence of Klein tunneling dominated transport in p-n-p junctions. Both the resistance and the Fano factor show broad resonance peaks due to the presence of quasi bound states. This feature is washed out by the disorder when the mean free path becomes of the order of the d…
The magnetic properties of disordered graphene and irradiated graphite are systematically studied using a combination of mean-field Hubbard model and first-principles calculations. By considering large-scale disordered models of graphene, I conclude that only single-atom defects can induce ferromagnetism in graphene-based materials. The preserved stacking order of graphene layers is shown to be another necessary condition for achieving a finite net magnetic moment of irradiated graphite. Ab initio calculations of hydrogen binding and diffusion and of interstitial-vacancy recombination further …
We investigate the conductivity $σ$ of graphene nanoribbons with zigzag edges as a function of Fermi energy $E_F$ in the presence of the impurities with different potential range. The dependence of $σ(E_F)$ displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of $σ(E_F)$ and a wide dip near the Dirac point, due to the special properties of long range potenti…
Off-diagonal disorder with random hopping between the sublattices of a bipartite lattice is described by a Hamiltonian which has chiral (sub-lattice) symmetry. The energy spectrum is symmetric around E=0 and for odd total number of lattice sites an isolated zero mode always exists, which coincides with the mobility edge of an Anderson transition in two dimensions(2D). In the chiral orthogonal symmetry class BDI we compute the fractal dimension $D_{2}$ of the zero mode for graphene samples with edges. In the absence of disorder $D_{2}=1$, which corresponds to a one-dimensional edge states, whil…
Using the transfer matrix method, we study the conductance of the chiral particles through a monolayer graphene superlattice with long-range correlated disorder distributed on the potential of the barriers. Even though the transmission of the particles through graphene superlattice with white noise potentials is suppressed, the transmission is revived in a wide range of angles when the potential heights are long-range correlated with a power spectrum $S(k)\sim1/k^β$. As a result, the conductance increases with increasing the correlation exponent values gives rise a metallic phase. We obtain a …
A graphene antidot lattice, created by a regular perforation of a graphene sheet, can exhibit a considerable band gap required by many electronics devices. However, deviations from perfect periodicity are always present in real experimental setups and can destroy the band gap. Our numerical simulations, using an efficient linear-scaling quantum transport simulation method implemented on graphics processing units, show that disorder that destroys the band gap can give rise to a transport gap caused by Anderson localization. The size of the defect induced transport gap is found to be proportiona…
We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimal non-zero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disor…
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…
We analyze the full transport statistics of graphene with smooth disorder at low dopings. First we consider the case of 1D disorder for which the transmission probability distribution is given analytically in terms of the graphene-specific mean free path. All current cumulants are shown to scale with system parameters (doping, size, disorder strength and correlation length) in an identical fashion for large enough systems. In the case of 2D disorder, numerical evidence is given for the same kind of identical scaling of all current cumulants, so that the ratio of any two such cumulants is unive…
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 calculate the heat flux and electron-phonon thermal conductance in a disordered graphene sheet, going beyond a Fermi's Golden rule approach to fully account for the modification of the electron-phonon interaction by disorder. Using the Keldysh technique combined with standard impurity averaging methods in the regime $k_F l >> 1$ (where $k_F$ is the Fermi wavevector, l the mean free path), we consider both scalar potential (i.e. deformation potential) and vector potential couplings between electrons and phonons. We also consider the effects of electronic screening at the Thomas-Fermi level. …
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.
The discovery of graphene, a single monolayer of graphite, has closed the discussion on stability of 2D crystals. Although thermal fluctuations of such crystals tend to destroy the long-range order in the system, the crystal can be stabilized by strong anharmonicity effects. This competition is the central issue of the crumpling transition, i.e., a transition between flat and crumpled phases. We show that anharmonicity-controlled fluctuations of a graphene membrane around equilibrium flat phase lead to unusual elastic properties. In particular, we demonstrate that stretching $ξ$ of a flake of …
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 analysis of the electron localization properties in doped graphene is performed by doing a numerical multifractal analysis. By obtaining the singularity spectrum of a tight-binding model, it is found that the electron wave functions present a multifractal behavior. Such multifractality is preserved even for second neighbor interaction, which needs to be taken into account if a comparison is desired with experimental results. States close to the Dirac point have a wider multifractal character than those far from this point as the impurity concentration is increased. The analysis of the resul…
We study two lattice models, the honeycomb lattice (HCL) and a special square lattice (SQL), both reducing to the Dirac equation in the continuum limit. In the presence of disorder (gaussian potential disorder and random vector potential), we investigate the behaviour of the density of states (DOS) numerically and analytically. While an upper bound can be derived for the DOS on the SQL at the Dirac point, which is also confirmed by numerical calculations, no such upper limit exists for the HCL in the presence of random vector potential. A careful investigation of the lowest eigenvalues indeed …
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 present a microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size. The derivation leads to a renormalized, position-dependent diffusion coefficient. The position dependence of the latter is due to the position dependence of return probability in a bounded medium.
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…
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.
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…
The low energy spectrum of a zigzag graphene ribbon contains two gapless bands with highly non-linear dispersion, $ε(k)=\pm |π-k|^W$, where $W$ is the width of the ribbon. The corresponding states are located at the two opposite zigzag edges. Their presence reflects the fact that the clean ribbon is a quasi one dimensional system naturally fine-tuned to the topological {\em multicritical} point. This quantum critical point separates a topologically trivial phase from the topological one with the index $W$. Here we investigate the influence of the (chiral) symmetry-preserving disorder on such a…
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 electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder at half filling. We show that the transport properties of the system depend strongly on the symmetry of disorder. We find that the localization is ineffective if the randomness preserves one of the chiral symmetries of the clean Hamiltonian or does not mix valleys. We obtain the exact value of minimal conductivity $4e^2/πh$ in the case of chiral disorder. For long-range disorder (decoupled valleys), we derive the effective field theory. In the case of smooth random potential, it is…
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 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 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…
Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is obtained, which shows that absorption suppresses the fluctuations of the phase. The applicability of the random phase approximation is discussed.
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 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 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 experimentally investigate the impact of uncorrelated composite and structural disorder in photonic graphene. We find that in case of structural disorder not only chiral symmetry, but also the vanishing of the density of states at zero energy is preserved. This is in contrast to composite disorder, where chiral symmetry as well as the vanishing of the density of states are destroyed. Our observations are experimentally proven by exciting edge states at the bearded edge in disordered photonic graphene.
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…
Our study of the evolution of transmission eigenvalues, due to changes in various physical parameters in a disordered region of arbitrary dimensions, results in a generalization of the celebrated DMPK equation. The evolution is shown to be governed by a single complexity parameter which implies a deep level of universality of transport phenomena through a wide range of disordered regions. We also find that the interaction among eigenvalues is of many body type that has important consequences for the statistical behavior of transport properties.
The electronic properties of non-interacting particles moving on a two-dimensional bricklayer lattice are investigated numerically. In particular, the influence of disorder in form of a spatially varying random magnetic flux is studied. In addition, a strong perpendicular constant magnetic field $B$ is considered. The density of states $ρ(E)$ goes to zero for $E\to 0$ as in the ordered system, but with a much steeper slope. This happens for both cases: at the Dirac point for B=0 and at the center of the central Landau band for finite $B$. Close to the Dirac point, the dependence of $ρ(E)$ on t…
The dynamic conductivity σ(ω) of graphene in the presence of diagonal white noise disorder and quantizing magnetic field B is calculated. We obtain analytic expressions for σ(ω) in various parametric regimes ranging from the quasiclassical Drude limit corresponding to strongly overlapping Landau levels (LLs) to the extreme quantum limit where the conductivity is determined by the optical selection rules of the clean graphene. The nonequidistant LL spectrum of graphene renders its transport characteristics quantitatively different from conventional 2D electron systems with parabolic spectrum. S…
