Impurities In Graphene Research Articles

Anomalous induced density of supercritical Coulomb impurities in graphene under strong magnetic fields

Anomalous induced density of supercritical Coulomb impurities in graphene under strong magnetic fields

Impurities in graphene and their influence on the Casimir interaction

Impurities in graphene and their influence on the Casimir interaction

Coulomb impurities in graphene driven by ultrashort electromagnetic pulses: excitation, ionization, and pair creation

We provide a theory for electronic transitions induced by ultrashort electromagnetic pulses in two-dimensional artificial relativistic atoms which are created by a charged impurity in a gapped graphene monolayer. Using a non-perturbative sudden-perturbation approximation, we derive and discuss analytical expressions for the probabilities for excitation, ionization and electron-hole pair creation in this system.

Challenges for Scaling Up Electron-Beam Manipulation of Graphene Impurities.

Challenges for Scaling Up Electron-Beam Manipulation of Graphene Impurities.

A Modified Wet Transfer Method for Eliminating Interfacial Impurities in Graphene.

Graphene has immense potential as a material for electronic devices owing to its unique electrical properties. However, large-area graphene produced by chemical vapor deposition (CVD) must be transferred from the as-grown copper substrate to an arbitrary substrate for device fabrication. The conventional wet transfer technique, which uses FeCl3 as a Cu etchant, leaves microscale impurities from the substrate, and the etchant adheres to graphene, thereby degrading its electrical performance. To address this limitation, this study introduces a modified transfer process that utilizes a temporary UV-treated SiO2 substrate to adsorb impurities from graphene before transferring it onto the final substrate. Optical microscopy and Raman mapping confirmed the adhesion of impurities to the temporary substrate, leading to a clean graphene/substrate interface. The retransferred graphene shows a reduction in electron-hole asymmetry and sheet resistance compared to conventionally transferred graphene, as confirmed by the transmission line model (TLM) and Hall effect measurements (HEMs). These results indicate that only the substrate effects remain in action in the retransferred graphene, and most of the effects of the impurities are eliminated. Overall, the modified transfer process is a promising method for obtaining high-quality graphene suitable for industrial-scale utilization in electronic devices.

Suppression of Intervalley Coupling in Graphene via Potassium Doping.

The quantum interference patterns induced by impurities in graphene can form the (√3 × √3)R30° superlattice with intervalley scattering. This superlattice can lead to the folded Dirac cone at the center of Brillouin zone by coupling two non-equivalent valleys. Using angle-resolved photoemission spectroscopy (ARPES), we report the observation of suppression of the folded Dirac cone in mono- and bilayer graphene upon potassium doping. The intervalley coupling with chiral symmetry broken can persist upon a light potassium-doped level but be ruined at the heavily doped level. Meanwhile, the folded Dirac cone can be suppressed by the renormalization of the Dirac band with potassium doping. Our results demonstrate that the suppression of the intervalley scattering pattern by potassium doping could pave the way toward the realization of novel chiraltronic devices in superlattice graphene.

Impurity states and indirect exchange interaction in irradiated graphene

We theoretically investigate the impurity levels and exchange interaction between magnetic impurities in graphene driven by an off-resonant circularly polarized light field. Our analysis captures the non-perturbative effects resulting from scattering with magnetic impurities with a strong onsite potential. Under irradiation, a dynamical band gap opens up at the Dirac point, allowing impurity levels to exist inside the gap. These impurity levels are shown to give rise to a resonance feature in the exchange energy for impurities located either at the same or different sublattices. The exchange interaction also shows a wider spatial range of antiferromagnetic behavior due to irradiation. Our work demonstrates that the exchange energy of magnetic impurities in graphene is extensively tunable by light irradiation in the presence of strong potential scattering.

Beam-driven dynamics of aluminium dopants in graphene

Substituting heteroatoms into graphene can tune its properties for applications ranging from catalysis to spintronics. The further recent discovery that covalent impurities in graphene can be manipulated at atomic precision using a focused electron beam may open avenues towards sub-nanometer device architectures. However, the preparation of clean samples with a high density of dopants is still very challenging. Here, we report vacancy-mediated substitution of aluminium into laser-cleaned graphene, and without removal from our ultra-high vacuum apparatus, study their dynamics under 60 keV electron irradiation using aberration-corrected scanning transmission electron microscopy and spectroscopy. Three- and four-coordinated Al sites are identified, showing excellent agreement with ab initio predictions including binding energies and electron energy loss spectrum simulations. We show that the direct exchange of carbon and aluminium atoms predicted earlier occurs under electron irradiation, although unexpectedly it is less probable than the same process for silicon. We also observe a previously unknown nitrogen–aluminium exchange that occurs at Al–N double-dopant sites at graphene divacancies created by our plasma treatment.

Coexistence of electron whispering-gallery modes and atomic collapse states in graphene/WSe2 heterostructure quantum dots

The relativistic massless charge carriers with a Fermi velocity of about c/300 in graphene enable us to realize two distinct types of resonances (here, c is the speed of light in vacuum). One is the electron whispering-gallery mode in graphene quantum dots arising from the Klein tunneling of the massless Dirac fermions. The other is the atomic collapse state, which has never been observed in experiment with real atoms due to the difficulty of producing heavy nuclei with charge Z > 170; however, they can be realized near a Coulomb impurity in graphene with a charge Z ≥ 1 because of the “small” velocity of the Dirac excitations. Here we demonstrate that both the electron whispering-gallery modes and atomic collapse states coexist in graphene/WSe2 heterostructure quantum dots due to the Coulomb-like potential near their edges. By applying a perpendicular magnetic field, we explore the evolution from the atomic collapse states to unusual Landau levels in the collapse regime.

Direct Observation of Global Elastic Intervalley Scattering Induced by Impurities on Graphene.

The scattering process induced by impurities in graphene plays a key role in transport properties. Especially, the disorder impurities can drive the ordered state with a hexagonal superlattice on graphene by electron-mediated interaction at a transition temperature. Using angle-resolved photoemission spectroscopy (ARPES), we reveal that the epitaxial monolayer and bilayer graphene with various impurities display global elastic intervalley scattering and quantum interference below the critical temperature (34 K), which leads to a set of new folded Dirac cones at the Brillouin-zone center by mixing two inequivalent Dirac cones. The Dirac electrons generated from intervalley scattering without chirality can be due to the breaking of the sublattice symmetry. In addition, the temperature-dependent ARPES measurements indicate the thermal damping of quantum interference patterns from Dirac electron scattering on impurities. Our results demonstrate that the electron scattering and interference induced by impurities can completely modulate the Dirac bands of graphene.

Near-field probing of dielectric screening by hexagonal boron nitride in graphene integrated on silicon photonics

Hexagonal boron nitride (hBN) is one of the most suitable 2D materials for supporting graphene in electronic devices, and it plays a fundamental role in screening out the effect of charge impurities in graphene in contrast to inhomogeneous supports such as silicon dioxide (SiO2). Although many interesting surface science techniques such as scanning tunneling microscopy (STM) revealed dielectric screening by hBN and emergent physical phenomena were observed, STM is only appropriate for graphene electronics. In this paper, we demonstrate the dielectric screening by hBN in graphene integrated on a silicon photonic waveguide from the perspective of a near-field scanning optical microscopy (NSOM) and Raman spectroscopy. We found shifts in the Raman spectra and about three times lower slope decrease in the measured electric near-field amplitude for graphene on hBN relative to that for graphene on SiO2. Based on finite-difference time-domain simulations, we confirm lower electric field slope and scattering rate in graphene on hBN, which implies dielectric screening, in agreement with the NSOM signal. Graphene on hBN integrated on silicon photonics can pave the way for high-performance hybrid graphene photonics.

Persistent Friedel oscillations in graphene due to a weak magnetic field

Two opposite chiralities of Dirac electrons in a two-dimensional (2D) graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/{r}^{3}$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is dominant in a parametrically large spatial interval ${p}_{0}^{\ensuremath{-}1}\ensuremath{\lesssim}r\ensuremath{\lesssim}{k}_{F}{l}^{2}$, where $l$ is the magnetic length, ${k}_{F}$ is Fermi momentum, and ${p}_{0}^{\ensuremath{-}1}={({k}_{F}l)}^{4/3}/{k}_{F}$. Moreover, in this interval, the field-dependent oscillations do not decay with distance. The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.

Nonadiabatic Effects on Defect Diffusion in Silicon-Doped Nanographenes.

Single atom impurities in graphene, substitutional silicon defects in particular, have been observed to diffuse under electron beam irradiation. However, the relative importance of elastic and inelastic scattering in facilitating their mobility remains unclear. Here, we employ excited-state electronic structure calculations to explore potential inelastic effects, and find an electronically nonadiabatic excited-state silicon diffusion pathway involving "softened" Si-C bonding that presents an ∼2 eV lower diffusion barrier than the ground-state pathway. Beam-induced transition rates to this state indicate that the excited-state pathway is accessible through irradiation of the defect site. However, even in the limit of fully elastic scattering, upward nonadiabatic transitions are also possible along the diffusion coordinate, increasing the diffusion barrier and further demonstrating the potential for electronic nonadiabaticity to influence beam-induced atomic transformations in materials. We also propose some experimentally testable signatures of such excited-state pathways.

Non-uniform self-folding of impure graphene

Planar graphene with extreme flexibility folds into three-dimension structures, holding promises in quantum- and nano-electronics with interesting geometries and properties. However, it is challenging to synthesize high-quality and uniform graphene on a large scale. The inevitable inhomogeneity, such as geometry variation and material impurity, yields imperfect graphene and tunable folded structures. This enables the diverse design of nanostructures with targeted configurations and engineered performances. The mechanics of non-uniform self-folding of impure graphene is explored through a finite-deformation varying-section beam model, the critical folding conditions, folded profiles, and maximum strains dependent on the non-uniform half-length are theoretically determined. Molecular dynamics (MD) simulations are performed to verify theoretical solutions. Our study is helpful for the design of programmable quantum- and nano-electronics to achieve desired properties.

The critical transition of Coulomb impurities in gapped graphene

The effect of supercritical charge impurities in graphene is very similar to the supercritical atomic collapses in QED for Z > 137, but with a much lower critical charge. In this sense graphene can be considered as a natural testing ground for the analysis of quantum field theory vacuum instabilities. We analyze the quantum transition from subcritical to supercritical charge regimes in gapped graphene in a common framework that preserves unitarity for any value of charge impurities. In the supercritical regime it is possible to introduce boundary conditions which control the singular behavior at the impurity. We show that for subcritical charges there are also non-trivial boundary conditions which are similar to those that appear in QED for nuclei in the intermediate regime 118 < Z < 137. We analyze the behavior of the energy levels associated to the different boundary conditions. In particular, we point out the existence of new bound states in the subcritical regime which include a negative energy bound state in the attractive Coulomb regime. A remarkable property is the continuity of the energy spectral flow under variation of the impurity charge even when jumping across the critical charge transition. We also remark that the energy levels of hydrogenoid bound states at critical values of charge impurities act as focal points of the spectral flow.

The wrinkle formation in graphene on transition metal substrate: a molecular dynamics study

ABSTRACT To explore the mechanism of the wrinkle formation in graphene on transition metal substrate, a molecular dynamics (MD) simulation package that allows us to simulate systems of millions of atoms was developed. Via the MD simulation, we reveal the detailed kinetics of wrinkles formation on a Cu substrate under compressive strain, from nucleation to one-dimensional propagation and then the splitting of a large wrinkle to a few smaller ones, which is in good conformity with experimental observation. Further study reveals that both friction and the adhesion between graphene and Cu substrate are critical for the wrinkle formation and wrinkles can be easily formed with a lower frictional force and/or a smaller adhesion. Finally, we have shown that impurities in graphene or substrates can greatly facilitate the nucleation of wrinkles. The systematic exploration of the wrinkle formation in graphene on a substrate is expected to facilitate the experimental designs for the controllable synthesis of high-quality graphene.

Electronic properties of graphene with point defects (Review Article)

This review is an attempt to consistently examine the electronic spectrum of graphene containing defects (such as adsorbed atoms, substitutional atoms, vacancies) that can be adequately described using the Lifshitz model. Therefore, the known Hamiltonian of this model is chosen for the case of two-dimensional relativistic electrons, and the criteria for the appearance of an impurity resonance near the Dirac point are provided. The theory of concentration band structure transformation in graphene is outlined, from which it follows that a transport gap opens in the vicinity of the impurity resonance energy when a specific value of the impurity concentration is reached. Along the way, the question of whether or not it is possible (or impossible) for Dirac quasiparticles to become localized in such a spatially disordered system is analyzed. Based on this, it is feasible to explain and describe the recently observed in impure graphene phenomenon of metal-insulator transition, which turns out to be a direct consequence of the system’s Fermi energy falling into the domain of the transport gap. The concept of local spectrum rearrangement, which can also unfold as the defect concentration increases, is introduced and justified for graphene. We formulate the physical reasons why the minimum of graphene’s low-temperature conductivity dependence on the Fermi energy of electrons does correspond to the impurity resonance energy, and not the Dirac point, as it has been claimed in a number of theoretical and experimental studies. Furthermore, the mentioned minimum value proves to be not universal, but is dependent, instead, on the concentration of defects. The analytical considerations of the impurity effects are accompanied by numerical simulations of the examined system, and a complete correspondence between these two approaches is established as a result. In particular, the general scenarios of spectrum rearrangement, electron state localization, as well as of effects having a local nature, are confirmed.

Kondo effect due to a hydrogen impurity in graphene: A multichannel Kondo problem with diverging hybridization

We consider the Kondo effect arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the $C_{3}$ rotation symmetry, and we only retain the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) $\propto 1/ [ | \omega \ | \ln ^{2}( \Lambda /| \omega \ | \ ) \ ] $ near the Dirac point $\omega \rightarrow 0$ even though the bulk density of states vanishes linearly. We study the resulting 3-impurity multi-channel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-$1/2$ doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity.

Thermoelectric and electronic properties of B-doped graphene nanoribbon

The effect of concentration and position of boron atoms as impurities in graphene nanoribbons have been studied through density functional theory (DFT) and the Landauer approach. For this purpose, we designed a graphene nanoribbon doped with three different concentrations of boron atoms and calculated the density of states (DOS), electronic current, and thermopower. The comparison between the DOS curve of the pure graphene and that of the boron-doped graphene shows that the presence of boron atoms as impurities in graphene has caused an energy gap near the Fermi energy. Moreover, the study of the I–V characteristics shows that not only the current quantization is established, but also the reduction in conductivity caused by doping with boron atoms can be observed; however, this reduction is not sensitive to the concentration of boron atoms. In addition, the changes of the Seebeck coefficient shows that in both pure and boron-doped graphene, the curve has a minimum value at the temperature of 10 K, which decreases to a lower value by increasing the concentration of boron atoms. Generally, the result of calculations shows that by increasing the boron concentration, not only the energy gap of graphene is changed, but also several changes appear in its thermoelectric properties that can be attributed to the impurity potential distribution. The results of this study can be effectively used for designing semiconductor electronic devices based on the graphene nanoribbon.

Electron-Beam Manipulation of Lattice Impurities in Graphene and Single-Walled Carbon Nanotubes

Electron-Beam Manipulation of Lattice Impurities in Graphene and Single-Walled Carbon Nanotubes