Session L37: Focus Session: Vacancy and Grain Boundary Effects in Graphene

Electrical Properties of Overlapped Graphene Grain Boundaries Probed by Raman Spectroscopy

The effect of grain boundaries and wrinkles on the electrical properties of polycrystalline graphene is pronounced. Here we investigate the stitching between grains of polycrystalline graphene, specifically, overlapping of layers at the boundaries, grown by chemical vapor deposition (CVD) and subsequently doped by the oxidized Cu substrate. We analyze overlapped regions between 60 -- 220 nm wide via Raman spectroscopy, which reveals their structure to be AB--stacked bilayers. The Raman spectra from the overlapped regions are distinctively different from bilayer graphene and exhibit splitting of the G band peak. The degree of splitting, peak widths, and peak intensities depend on the width of the overlapped layer. We attribute these features to inhomogeneous doping by charge carriers (holes) across the overlapped grain boundaries via the oxidized Cu substrate. As a result, the Fermi level at the overlapped grain boundaries lies between 0.3 and 0.4 eV below the charge neutrality point. The dependence of charge distribution on the width of overlapping of grain boundaries may have strong implications for the growth of large-area graphene with enhanced conductivity.   

Vacancy vacancy interactions in graphene using first principles calculations

We employ first principles calculations to study the defect induced magnetism on monolayer graphene sheet. Removal of single, double and triple carbon atoms from a 6 $\times$ 6 monolayer graphene sheet gives magnetic moment (MM) comparable with those reported in the literature. For single vacancy defect, MM value lies in between 1.4 and 1.6 $\mu_B$, depending on the type of lattice atoms ($\alpha$ or $\beta$). For triple vacancy, MM is 1.04 $\mu_B$. Detailed study of double vacancy in graphene layer with a removal of similar and different type of lattice atoms gives interesting results in terms of magnetic moment as well as in spin density distributions. For double vacancy our study gives magnetic moment values 0 and 3 $\mu_B$, depending on the position and lattice type of the removed atoms. Our study reveals that removal of near by same lattice type atoms ($\alpha$ type) also leads to 0 magnetic moment, same as that of the removal of different lattice type atoms ($\alpha$ and $\beta$, irrespective of the distances). Here the distance between the removed two $\alpha$ type atoms is 2.46 \AA.   

Measuring the charge of a defect in graphene using atomic force microscopy

Graphene exhibits linear dispersion at the Dirac point, leading to novel properties that can be further tailored by the introduction of defects into the honeycomb lattice. In this work, we created vacancies on epitaxial graphene/SiC(0001) using N and Ar plasma, and studied the atomic structure of these defects using non-contact atomic force microscopy with a Q-plus sensor and density functional theory (DFT) calculations. We also determined charges carried by the vacancy defects by local contact potential measurements. These results and comparisons with DFT calculations will be discussed at the meeting.   

Defect-mediated coupling between graphene monolayer and hexagonal boron nitride sheet

Hexagonal boron nitride (hBN) offers an ideal substrate for graphene-based devices and promises to deliver higher device performances. A monolayer of graphene will be weakly coupled to a hBN substrate, but defects between the layers or within the hBN substrate are likely to enhance this coupling. We thus employed first-principles calculations to determine what effect such defects would have on the structural and electronic properties of graphene. We show in our paper that a boron (nitrogen) monovacancy in the hBN layer gives rise to p-doped (n-doped) graphene and that metal atom impurities may increase the energy of the Fermi level of graphene. We also demonstrate that the presence of monovacancies and some impurity atoms could induce residual scattering. However, we found that small triangular defect in hBN are unlikely to result in significant changes in the electronic transport of graphene.   

Gate-induced edge-state gap opening in an irradiated graphene nano-ribbon

Graphene undergoes topological phase transition when irradiated by a circularly polarized light. Dispersive helical edge states in both zigzag and armchair graphene nano-ribbons (ZGNR/AGNR) are the signatures. It is of interest to drive the system out-of the edge-state regime by electrical means. To this end, we propose a gate-potential configuration that covers part of the ribbon. For the case of ZGNR, the gate potential is shown to tune the degree of hybridization between edge states formed at opposite edges of the ribbon, leading eventually to edge-state gap opening. For the case of AGNR, the gate potential is less effective. The physics behind our findings will be discussed and supported by both numerical and analytical analysis.   

Electron Beam Irradiation Modulated Graphene Electronic Devices

We report controllable graphene doping using focused electron beams. Graphene field-effect-transistor (FET) devices with tunable electronic properties have been fabricated in a Scanning Electron Microscope (SEM). The doping state of graphene can be varied from electron to hole type at different electron beam energies (0.5keV to 30keV). The graphene FET devices exhibit high carrier concentrations ($\sim$ 5x10$^{12}$cm$^{-2})$, high mobility ($\sim$ 5x10$^{3}$cm$^{2}$/V$\cdot$s) and remain quite stable in vacuum. It is found that substrate charging and the induced internal electrical field is responsible for the doping effect. This enables a high spatial resolved, non-destructive and tunable manipulation for graphene electronic device prototyping. Graphene devices based on multi-doped p-n junctions and fine super-lattice structures have also been demonstrated.   

Graphene grain boundary resistivity revealed by scanning tunneling potentiometry

All large-scale graphene films contain extended topological defects dividing graphene into domains or grains. Here, we study grain boundary (GB) resistivity in CVD graphene on Cu subsequently transferred to a SiO2 substrate. By using a scanning tunneling potentiometry (STP) setup with a cryogenic four-probe STM, the spatial variation of the local electrochemical potential is resolved across individual GBs on a graphene surface in the presence of a current [1]. The 2D distributions of electric field and conductivity were then numerically extracted by solving conduction equations. The derived conductivity of individual grains was compared to that measured with microscopic four-probe STM method to provide a model-independent determination of conductivity map for specific type of defect in graphene. The resistance of a GB is found to change with the width of the disordered transition region between adjacent grains. A quantitative modeling of boundary resistance reveals the increased electron Fermi wave vector within the boundary region, possibly due to boundary induced charge density variation. [1] K. W. Clark et al. ACS Nano 2013, 7, 7956   

Symmetry protected low energy electronic states in graphene grain boundaries

We study graphene grain boundaries with the goal of predicting whether they support symmetry protected low energy electronic states localized at the boundary. Starting from a structural model for a grain boundary treated in the short range tight binding limit, we provide an algorithm for generating a chiral operator that anticommutes with the full Hamiltonian. For grain boundaries with nonbipartite lattice structures this operator is highly nonlocal. We identify two classes of grain boundaries: those that admit this chiral representation and those that do not. In the former case a zero energy electronic state is required by symmetry. We compare our results with electronic structures computed for various grain boundaries presented in the literature.   

Spanning graphene to carbon-nitride: A 2-D semiconductor alloy system of carbon and nitrogen

With the explosion of materials that form 2-D structures in the past few years, there have been a much more diverse ecosystem of combinations of characteristics to explore. Yet with the majority of materials investigated, the properties are fixed according to the composition of the material. Ideally, one wishes to have a tunable system similar to the semiconductor alloy systems, such as Al$_{\mathrm{x}}$Ga$_{\mathrm{1-x}}$As. There have been some theoretical studies of transition metal dichalogenides, none have been reported experimentally as of this writing. The tertianary alloy of BCN has been synthesized, however it was found that the boron had the tendency to cause phase segregation of the material into domains of graphene and boron nitride. Here we will report on the synthesis of non-phase seperated carbon-nitrogen 2D alloys ranging from graphene (E$_{\mathrm{g}}=$0 eV) to carbon-nitride, or melon, (E$_{\mathrm{g}}=$2.7 eV). We will report on synthesis methods and a summary of relevant electronic and material properties of selected alloys.   

Topological Aspects of Charge-Carrier Transmission across Grain Boundaries in Graphene

Dislocations and grain boundaries are intrinsic topological defects of large-scale polycrystalline samples of graphene. These structural irregularities have been shown to strongly affect electronic transport in this material. Here, we report a systematic investigation of the transmission of charge carriers across the grain-boundary defects in polycrystalline graphene by means of the Landauer-B\"uttiker formalism within the tight-binding approximation. Calculations reveal a strong suppression of transmission at low energies upon decreasing the density of dislocations with the smallest Burgers vector ${\mathbf{b}}=(1,0)$. The observed transport anomaly is explained from the point of view of resonant back-scattering due to localized states of topological origin. These states are related to the gauge field associated with all dislocations characterized by ${\mathbf{b}}=(n,m)$ with $n-m\neq3q$ ($q\in Z$). Our work identifies an important source of charge-carrier scattering caused by the topological defects present in large-area graphene samples produced by chemical vapor deposition. \\[4pt] Reference: F. Gargiulo and O. V. Yazyev, arXiv:1307.6746.   

Tunable Anderson Localization in Hydrogenated Graphene Based on the Electric Field Effect: First-Principles Study

We present a mechanism for reversible switching of the Anderson localization (AL) of electrons in hydrogenated graphene through modulation of the H coverage on graphene by external electric fields. The main idea is to exploit the unique acid-base chemistry (i.e., proton transfer reaction) between NH$_{\mathrm{3}}$ gas and hydrogenated graphene, which can be controlled by applying perpendicular electric fields. The proposed field-induced control of disorder in hydrogenated graphene not only has scientific merits in a systematic study of AL of electrons in grapheme but can also lead to new insight into the development of a new type of transistor based on reversible on/off switching of AL. Furthermore, the reversible and effective tuning of the H coverage on graphene should be useful for tailoring material properties of weakly hydrogenated graphene.   

Drift of Dirac points in defected graphene

Graphene's remarkable electronic properties are due to isotropic hopping between nearest-neighbor carbon atoms on a honeycomb lattice. If anisotropic hopping is introduced, Dirac points move in reciprocal space away from \textbf{K} and \textbf{K}'. In this work, we investigate the effect of periodic defects on the electronic structure of graphene using both analytic theory and numerical \textit{ab initio} computations. Our tight-binding model suggests that if the defect has a preferred direction, or anisotropy, the Dirac points move in reciprocal space. Analytic predictions for the magnitude and direction of drift are in excellent agreement with \textit{ab initio} calculations. In addition, we show that a semimetal-to-insulator transition occurs when the Dirac points drift onto certain high symmetry points of the supercell Brillouin zone.   

Exchange coupling between localized defect states in graphene nanoflakes

Graphene nanoflakes are interesting because electrons are naturally confined in these quasi zero-dimensional structures, thus eluding the need for a bandgap. Defects inside the graphene lattice lead to localized states and the spins of two such localized states may be used for spintronics. We perform a tight-binding description on the entire system and, by virtue of a Schrieffer-Wolff-transformation on the bonding and antibonding states, we extract the coupling strength between the localized states. The coupling strength allows us to estimate the exchange coupling, which governs the dynamics of singlet-triplet spintronics.   

Spatially-resolved thermopower of graphene: role of boundary and defects

We show a spatially-resolved thermopower of graphene on epitaxial graphene of SiC using a scanning tunneling microscopy (STM) method. A temperature difference between the tip and sample induces a thermovoltage, and it reflects a local variation of thermopower with atomic resolution. The epitaxial graphene shows a high thermoelectric power of 42 uV/K with a large change (9.6uV/K) at the monolayer-bilayer boundary. Since the thermovoltage is proportional to the logarithmic derivative of the local density of the state of sample, the thermovoltage map is sufficiently sensitive to distinguish electronic properties at the boundaries and defects. For instance, a thermovoltage map discloses a Fermi level shift toward the Dirac point near the step edge and long-wavelength Friedel oscillations of the bilayer terrace adjacent to the step. As a result, the thermopower distribution measurement with STM allows probing of the electronic, thermoelectric, and structural properties down to the individual defect level [1]. [1] Jewook Park et al., Nano Lett., 13 3269 (2013)   

Thermal and electrical conductivity of defective graphene: From grain boundaries to haeckelite

We study the effect of structural defects on the electronic and thermal conductivity of graphene from first-principles calcluations. After optimizing defective structures using density functional theory, we describe ballistic charge transport using the non-equilibrium Green's function formalism and thermal transport using non-equilibrium molecular dynamics simulations. We find that both the electrical conductance $G$ and thermal conductivity $\lambda$ depend sensitively on the nature, concentration and arrangement of 5-7 and 5-8 defects, which may form grain boundaries in the honeycomb lattice of graphene or, at large concentrations, convert it to haeckelite. Lines of defects in graphene turn both $\sigma$ and $\lambda$ anisotropic. In a defective structure of graphene nanoribbons interconnected by haeckelite strips, the electrical conductance $G$ increases, whereas the thermal conductivity is quenched by up to 1-2 orders of magnitude, mainly due to the reduced phonon mean free path. We conclude that defects play a profound role in the electrical and thermal transport of graphene.