Disorder In Graphene Research Articles

Combined Raman Spectroscopy and Magneto-Transport Measurements in Disordered Graphene: Correlating Raman D Band and Weak Localization Features

Although previous studies have reported the Raman and weak localization properties of graphene separately, very few studies have examined the correlation between the Raman and weak localization characterizations of graphene. Here, we report a Raman spectroscopy and low-magnetic-field electronic transport study of graphene devices with a controlled amount of defects introduced into the graphene by exposure to electron-beam irradiation and oxygen plasma etching. The relationship between the defect correlation length (LD), calculated from the Raman “D” peak, and the characteristic scattering lengths, Lϕ, Li and L*, computed from the weak localization effects measured in magneto-transport was investigated. Furthermore, the effect on the mean free path length due to the increasing amounts of irradiation incident on the graphene device was examined. Both parameters—including LD and Lϕ—decreased with the increase of irradiation, which was shown to be related to the increase of disorder through the concomitant decrease in the mean free path length, l. Although these are similar trends that have been observed separately in previous reports, this work revealed a novel nonlinear relationship between LD and Lϕ, particularly at lower levels of disorder. These findings are valuable for understanding the correlation between disorder in graphene and the phase coherence and scattering lengths of its charge carriers.

Enhanced Magnetoresistance Effect in Graphene Coupled to a Ferromagnetic Oxide with Charge Orbital Ordering

In this paper, we fabricated graphene/Fe3O4 heterostructure devices by stacking monolayer graphene on magnetite (Fe3O4) substrate and investigated their magneto-transport properties. Interestingly, graphene/Fe3O4 heterostructure devices exhibit a giant magnetoresistance (MR) of 70% at a low magnetic field of 0.65[Formula: see text]T and at 11[Formula: see text]K, which is three times greater than that of graphene on SiO2. Based on standard two-fluid model and LDA[Formula: see text]U simulation, we showed that the observed enhanced MR effect is due to the increased disorder in graphene induced through the charge polarization via the alignment of C atoms of graphene over the charge ordered B-site cations of Fe3O4. Our results demonstrate a potential way to enhance graphene MR effect through coupling graphene with a suitable substrate with charge orbital ordering.

Multiple excitations and temperature study of the disorder-induced Raman bands in MoS2

Raman spectroscopy has been extensively used to probe disorder in graphene and other carbon-related materials, and disorder-induced (DI) Raman bands are prominent even for low defect densities. The DI bands in MoS2 have been studied in the last years, but a multiple excitation study using laser excitation energies near the excitonic energies was still lacking. In this work, we investigate the low-frequency defect-induced Raman bands in MoS2 coming from the acoustic phonon branches near the Brillouin zone edge using samples produced by mechanical exfoliation and chemical vapor deposition, recorded with different laser excitation energies close to the resonance with the excitonic transitions, and measured at different temperatures, from 100 K to 400 K. Our results show that the defect-induced Raman processes are affected by both excitation energy and temperature. We find that the temperature of measurement affects the linear dependence between the intensities of the DI peaks and the defect concentration. In particular, we observed that the ratio of intensities of the DI longitudinal acoustic (LA) and transversal acoustic (TA) modes with respect to the first-order E′ mode is about the same for the two different samples when results are corrected by the defect density. We show in this work that the largest intensity of the DI peaks occurs for laser energies in the resonance with the excitonic transitions. Finally, we introduce a general expression that provides the parameters for the quantification of defects in MoS2 samples based on the intensity of the DI Raman bands, measured at different laser energies across the excitonic transitions.

Experimental evidence of disorder enhanced electron-phonon scattering in graphene devices

Induced disorder in graphene enables changes in electrical and thermal transport. It has been shown previously that disorder is very important for electron cooling in graphene through disorder-assisted electron-phonon scattering, particularly via the supercollisions process. Here we study electron-momentum relaxation due to electron-phonon scattering while increasing the degree of disorder. With in-situ scanning thermal microscopy we monitor the temperature rise in the constriction region of a bowtie-shaped graphene device while increasing the disorder by means of feedback-controlled voltage ramps at high-current densities. Analysis of the combined thermal and electrical measurements in the low bias regime shows that the relative change of the momentum scattering rate vs temperature, as measured at room temperature, increases with strong local disorder. By excluding other candidate mechanisms for this phenomenon, including a change of the charge carriers density and activation of optical phonons, we conclude that the increase we observe in the temperature-dependent component of the scattering rate is likely due to new acoustic phonon scattering channels that open up as disorder increases.

Effect of different preparation processes on tribological properties of graphene

Two processes of physical liquid phase stripping and chemical redox reduction were used to obtain graphene sheets. Fourier transform infrared spectroscopy and Raman spectroscopy test methods were used to compare and analyze the structure and disorder of graphene. The obtained graphene was modified with oleic acid and stearic acid. The dispersion stability of graphene as a lubricating oil additive was investigated by natural sedimentation method and spectrophotometry. The tribological properties of the graphene dispersion were investigated by a four-ball friction and wear tester. Scanning electron microscope and energy spectrometer were used to characterize and analyze the microscopic morphology and composition of the worn surface. The results showed that the modified liquid phase stripping graphene demonstrated the best anti-wear and anti-friction properties of the dispersion, the lowest friction coefficient is 0.0677, and the average friction coefficient is reduced by about 26%.

Defect Dynamics in Graphene

The experimental and theoretical study of graphene, two-dimensional (2D) graphite, is an extremely rapidly growing field of today's condensed matter research. Different types of disorder in graphene modify the Dirac equation leading to unusual spectroscopic and transport properties. The authors studied one of the disorders (i.e., grain boundaries) and formulated a theoretical model of graphene grain boundary by generalizing the two-dimensional graphene Dirac Hamiltonian model. In this model only, the authors considered the long-wavelength limit of the particle transport, which provides the main contribution to the graphene conductance. In this work, they derived the Hamiltonian in a rotated side dependent reference frame describing crystallographic axes mismatching at a grain boundary junction and showed that properties like energy spectrum are an independent reference frame. Also, they showed one of the topological property of graphene.

Comparative study of electron transfer on various graphene-metallic contacts

We have investigated Raman spectra of the G and 2D lines of a single-layer graphene (SLG) with metallic contacts. The shift of the G and 2D lines is correlated to two different factors. Before performing annealing treatment or annealing under low temperature, the electron transfer on graphene surface is dominated by nonuniform strain effect. As the annealing treatment is enhanced, however, a suitable annealing treatment can eliminate the nonuniform strain effect where the relative work function (WF) between graphene and metal becomes a main factor to determine electronic transfer. Moreover, it is confirmed that the optimized annealing treatment can also decrease effectively the structural defect and induced disorder in graphene due to metallic contacts.

Effect of E-beam irradiation on graphene sandwiched between h-BN layers

The potential of graphene for electronic applications originates owing to its exceptional room temperature carrier mobility. However, during the fabrication of electronic devices like field-effect transistors graphene is exposed to external environment that affects its carrier mobility. Also, the formation of dangling bonds at Si/SiO2 interface further degrades the mobility of graphene and hence influence the performance of graphene devices. In order to protect graphene from environmental conditions and preserve its fundamental electrical properties in such devices, here graphene is sandwiched between hBN layers (i.e. hBN/Graphene/hBN) and then the effect of e-beam irradiation on graphene structure is studied. To investigate structural disorder in graphene, Raman analysis was carried out which revealed no defects in graphene even for a high dose of e-beam irradiation. The electrical and magneto-transport measurements further confirmed the stability of these e-beam irradiated hBN-passivated graphene devices thereby demonstrating a mobility of 16,638 cm2/Vs and Quantum Hall plateaus at 9 T, respectively. Furthermore, different devices comprising Graphene/SiO2, Graphene/hBN and hBN/Graphene/hBN are studied for the interface analysis, which after e-beam irradiation revealed no defects and contaminations at the interfaces between hBN and graphene.

Understanding Sources of Electrical Disorder in Graphene Grown by Chemical Vapor Deposition for Wafer-Scale Device Applications

We present a comprehensive explanation of the sources of electrical disorder in graphene grown by chemical vapor deposition (CVD) and transferred onto SiO2 substrates. By correlating carrier concen...

Shape of the zeroth Landau level in graphene with nondiagonal disorder

Non-diagonal (bond) disorder in graphene broadens Landau levels (LLs) in the same way as random potential. The exception is the zeroth LL, $n=0$, which is robust to the bond disorder, since it does not mix different $n=0$ states within a given valley. The mechanism of broadening of the $n=0$ LL is the inter-valley scattering. Several numerical simulations of graphene with bond disorder had established that $n=0$ LL is not only anomalously narrow but also that its shape is very peculiar with three maxima, one at zero energy, $E=0$, and two others at finite energies $\pm E$. We study theoretically the structure of the states in $n=0$ LL in the presence of bond disorder. Adopting the assumption that the bond disorder is strongly anisotropic, namely, that one type of bonds is perturbed much stronger than other two, allowed us to get an analytic expression for the density of states which agrees with numerical simulations remarkably well. On the qualitative level, our key finding is that delocalization of $E=0$ state has a dramatic back effect on the density of states near $E=0$. The origin of this unusual behavior is the strong correlation of eigenstates in different valleys.

Raman spectroscopy of gallium ion irradiated graphene

The successful integration of graphene in future technologies, such as filtration and nanoelectronics, depends on the ability to introduce controlled nanostructured defects in graphene. In this work, Raman spectroscopy is used to investigate the induction of disorder in graphene via gallium ion beam bombardment. Two configurations of CVD-grown graphene samples are used: (i) graphene supported on a Si/SiO2 substrate, and (ii) graphene suspended on porous TEM grids. It is observed that the supported graphene experiences more damage in response to lower beam doses than suspended graphene. This phenomenon is attributed to the behaviour of the energetic ions impinging the sample. In suspended graphene, the ions pass through the graphene membrane once and disperse to the atmosphere, while in supported graphene, the ions embed themselves in the substrate causing swelling and backscattering events, hence increasing the induced disorder. In supported graphene, the ratio between the Gaussian D and G peaks attributed to amorphous carbon, and the Lorentzian D and G peaks attributed to graphene, (IDG/IDL) and (IGG/IGL), are suggested to be used to quantify the degree of amorphization. The results are relevant to the development of nanostructured graphene-based filtration or desalination membranes, as well as for graphene-based nanoelectronics.

Near-field coherence reveals defect densities in atomic monolayers

The ability to control the light-matter interaction in the deep subwavelength regime has fascinating consequences for material sciences and a range of photonics technologies. The statistical properties of emerging fields strongly depend on both the source of radiation and specific characteristics of the material system. Here we consider the coherence properties in the proximity of surfaces illuminated by strongly randomized optical fields and demonstrate that the spatial extent of near-field correlations depends on the density of defects in two-dimensional crystalline lattices. We also show that this effect can be used as an efficient elastic scattering method to characterize the density of defects in two-dimensional crystalline materials. Systematic experiments demonstrate the relationship between the spatial coherence length of scattered light and a characteristic length associated with structural disorder in graphene. The fact that one single layer of atoms can modify properties of electromagnetic radiation could lead to new means of controlling light at subwavelength scales and has implications for the emerging field of two-dimensional materials.

Dominant source of disorder in graphene: charged impurities or ripples?

Experimentally produced graphene sheets exhibit a wide range of mobility values. Both extrinsic charged impurities and intrinsic ripples (corrugations) have been suggested to induce long-range disorder in graphene and could be a candidate for the dominant source of disorder. Here, using large-scale molecular dynamics and quantum transport simulations, we find that the hopping disorder and the gauge and scalar potentials induced by the ripples are short-ranged, in strong contrast with predictions by continuous models, and the transport fingerprints of the ripple disorder are very different from those of charged impurities. We conclude that charged impurities are the dominant source of disorder in most graphene samples, whereas scattering by ripples is mainly relevant in the high carrier density limit of ultraclean graphene samples (with a charged impurity concentration less than about 10 ppm) at room and higher temperatures. Our finding is valuable to theoretical modelling of transport properties of not only graphene, but also other two-dimensional materials, as the thermal ripples are universal.

Bimodal Control of Heat Transport at Graphene-Metal Interfaces Using Disorder in Graphene.

Thermal energy transport across the interfaces of physically and chemically modified graphene with two metals, Al and Cu, was investigated by measuring thermal conductance using the time-domain thermoreflectance method. Graphene was processed using a He2+ ion-beam with a Gaussian distribution or by exposure to ultraviolet/O3, which generates structural or chemical disorder, respectively. Hereby, we could monitor changes in the thermal conductance in response to varying degrees of disorder. We find that the measured conductance increases as the density of the physical disorder increases, but undergoes an abrupt modulation with increasing degrees of chemical modification, which decreases at first and then increases considerably. Moreover, we find that the conductance varies inverse proportionally to the average distance between the structural defects in the graphene, implying a strong in-plane influence of phonon kinetics on interfacial heat flow. We attribute the bimodal results to an interplay between the distinct effects on graphene’s vibrational modes exerted by graphene modification and by the scattering of modes.

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.

Singularity of density of states induced by random bond disorder in graphene

We re-investigate the effect of random bond disorder on the density of states (DOS) in graphene. Our large-scale calculation supports that there exists a critical disorder value gbc dividing the DOS into two distinct structures. In the regime gb<gbc (gb is randomness of bond disorder), the DOS away from the Dirac point behaves like a power-law with positive exponent (α>0): ρ(E)∼ρ1|E|α (E is Fermi energy with respect to the Dirac point, ρ1 is a constant). In the regime gb>gbc, it is observed that DOS develops a peak structure at the Dirac point E=0. Through the finite-size scaling analysis, we elucidate that the DOS at the Dirac point diverges in the thermodynamics limit. Furthermore, it is found that the divergent behavior of DOS is sensitive to any on-site disorder which violates the chiral symmetry in graphene.

Lateral damage in graphene carved by high energy focused gallium ion beams

Raman mapping is performed to study the lateral damage in supported monolayer graphene carved by 30 keV focused Ga+ beams. The evolution of the lateral damage is tracked based on the profiles of the intensity ratio between the D (1341 cm−1) and G (1582 cm−1) peaks (ID/IG) of the Raman spectra. The ID/IG profile clearly reveals the transition from stage 2 disorder into stage 1 disorder in graphene along the direction away from the carved area. The critical lateral damage distance spans from &amp;lt;1 μm up to more than 30 μm in the experiment, depending on the parameters used for carving the graphene. The wide damage in the lateral direction is attributed to the deleterious tail of unfocused ions in the ion beam probe. The study raises the attention on potential sample damage during direct patterning of graphene nanostructures using the focused ion beam technique. Minimizing the total carving time is recommended to mitigate the lateral damage.

Long- versus Short-Range Scattering in Doped Epitaxial Graphene.

Tuning the electronic properties of graphene by adatom deposition unavoidably introduces disorder into the system, which directly affects the single-particle excitations and electrodynamics. Using angle-resolved photoemission spectroscopy (ARPES) we trace the evolution of disorder in graphene by thallium adatom deposition and probe its effect on the electronic structure. We show that the signatures of quasiparticle scattering in the photoemission spectral function can be used to identify thallium adatoms, although charged, as efficient short-range scattering centers. Employing a self-energy model for short-range scattering, we are able to extract a δ-like scattering potential δ = -3.2 ± 1 eV. Therefore, isolated charged scattering centers do not necessarily act just as good long-range (Coulomb) scatterers but can also act as efficient short-range (δ-like) scatterers; in the case of thallium, this happens with almost equal contributions from both mechanisms.

Electron supercollimation in graphene and Dirac fermion materials using one-dimensional disorder potentials.

Electron supercollimation, in which a wave packet is guided to move undistorted along a selected direction, is a highly desirable property that has yet to be realized experimentally. Disorder in general is expected to inhibit supercollimation. Here we report a counterintuitive phenomenon of electron supercollimation by disorder in graphene and related Dirac fermion materials. We show that one can use one-dimensional disorder potentials to control electron wave packet transport. This is distinct from known systems where an electron wave packet would be further spread by disorder and hindered in the potential fluctuating direction. The predicted phenomenon has significant implications in the understanding and applications of electron transport in Dirac fermion materials.

Modification on Single-Layer Graphene Induced by Low-Energy Electron-Beam Irradiation

In this work, we present studies of the effects of electron-beam irradiation on the modification of single-layer graphene. Micro-Raman spectra show that the D, D′, and D + G Raman bands, which are invisible for pristine graphene, appear after the graphenes are irradiated by low-energy electron-beam irradiation (10 keV), and the intensities of these peaks increase with increasing irradiation time, indicating disorder in graphene. The characteristics of G and 2D bands of graphene are also studied before and after irradiation. In the meantime, the height of graphene is studied by atomic force microscopy and found to increase for increasing irradiation time due to the contaminant deposition on graphene. The effects introduced by irradiation can be recovered partly by vacuum annealing. These results provide important information about the modification of graphene under electron-beam irradiation.