Session V11: Focus Session: Graphene Structure, Stacking, Interactions: Edges and Grain Boundaries

Theory and hierarchical calculations of [0001] tilt grain boundaries in graphene

Several experiments have revealed the presence of grain boundaries in graphene that may change its electronic and elastic properties. Here, we present a general theory for the structure of [0001] tilt grain boundaries in graphene based on the coincidence site lattice (CSL) theory. We show that the CSL theory uniquely classifies the grain boundaries in terms of the misorientation angle $\theta$ and periodicity $d$. The structure and formation energy of a large set of grain boundaries generated by the CSL theory for 0$^\circ < \theta < 60^\circ$ (up to 15 608 atoms) were optimized by a hierarchical methodology and validated by density functional calculations. We find that low-energy grain boundaries in graphene can be identified as dislocation arrays. In contrast to three-dimensional materials, the strain created by the grain boundary can be released via out-of-plane distortions that imply to an effective attractive interaction between dislocation cores. This leads to a (secondary) minimum structure at $\theta = 32.2^\circ$, where the grain boundary is made of a flat zigzag array of only 5-- and 7--rings. We discuss the importance of these findings for the interpretation of recent experimental results.   

Localized states at grain boundaries in graphite

Scanning Tunneling Microscopy and Spectroscopy at low temperature and in magnetic field was used to characterize the electronic states near grain boundaries on the surface of graphite. Topographic surface maps show the grain boundaries as narrow stripes within which the lattice is reconstructed into a periodic pattern whose period is determined by the relative orientation between adjacent grains. In spectroscopy the grain boundaries produce sharp peaks in the density-of-states at energies that are characteristic of the misorientation between adjacent grains. Spatial maps of the density-of-states at these peak energies show that the peaks correspond to electronic states that are localized on the grain boundaries. We will present measurements of these localized electronic states, their evolution with magnetic field and misorientation angle between grains. The experimental results will be compared with theoretical calculations.   

Altering graphene line defect properties using chemistry

First-principles calculations are presented of a fundamental topological line defect in graphene that was observed and reported in Nature Nanotech. 5, 326 (2010). These calculations show that atoms and smaller molecules can bind covalently to the surface in the vicinity of the graphene line defect. It is also shown that the chemistry at the line defect has a strong effect on its electronic and magnetic properties, e.g. the ferromagnetically aligned moments along the line defect can be quenched by some adsorbates. The strong effect of the adsorbates on the line defect properties can be understood by examining how these adsorbates affect the boundary-localized states in the vicinity of the Fermi level. We also expect that the line defect chemistry will significantly affect the scattering properties of incident low-energy particles approaching it from graphene.   

Imaging the Structure of Grains, Grain Boundaries, and Stacking Sequences in Single and Multi-Layer Graphene

Graphene can be produced by chemical vapor deposition (CVD) on copper substrates on up to meter scales [1, 2], making their polycrystallinity [3,4] almost unavoidable. By combining aberration-corrected scanning transmission electron microscopy and dark-field transmission electron microscopy, we image graphene grains and grain boundaries across six orders of magnitude. Atomic-resolution images of graphene grain boundaries reveal that different grains can stitch together via pentagon-heptagon pairs. We use diffraction-filtered electron imaging to map the shape and orientation of several hundred grains and boundaries over fields of view of a hundred microns. Single, double and multilayer graphene can be differentiated, and the stacking sequence and relative abundance of sequences can be directly imaged. These images reveal an intricate patchwork of grains with structural details depending strongly on growth conditions. The imaging techniques enabled studies of the structure, properties, and control of graphene grains and grain boundaries [5]. \\[4pt] [1] X. Li\textit{ et al.}, \textit{Science} \textbf{324}, 1312 (2009).\\[0pt] [2] S. Bae\textit{ et al.}, \textit{Nature Nanotechnol.} \textbf{5}, 574 (2010).\\[0pt] [3] J. M. Wofford,\textit{ et al.}, \textit{Nano Lett.}, (2010).\\[0pt] [4] P. Y. Huang, et al., \textit{Nature} \textbf{469}, 389--392 (2011); \textit{arXiv:1009.4714}, (2010)\\[0pt] [5] In collaboration with Pinshane Y. Huang, C. S. Ruiz-Vargas, A. M. van der Zande, A. W. Tsen, L. Brown, R. Hovden, F. Ghahari, W. S. Whitney, M.P. Levendorf, J. W. Kevek, S. Garg, J. S. Alden, C. J. Hustedt, Y. Zhu, N. Petrone, J. Hone, J. Park, P. L. McEuen   

Experimentally Controlling the Edge Termination of Graphene Nanoribbons

The edges of graphene exhibit several unique features, such as the presence of localized edge states, and are anticipated to be a powerful means of controlling the electronic properties of this two-dimensional material. Understanding such properties, however, requires a precise knowledge of the atomic-scale structure and chemical composition of the edge. In this work, the edges of graphene nanoribbons (GNRs) are controlled by hydrogen plasma and are investigated through a combination of high-resolution scanning tunneling microscopy (STM) and first-principles calculations. We recover the atomic structure of the edge termination in atom-by-atom fashion and establish the chemical nature of terminating functional groups at graphene edge segments of different orientation -- (i.e., zigzag, armchair and chiral). These results allow us to conclude that the edges of hydrogen-plasma-etched GNRs are generally free of structural reconstructions and are terminated by hydrogen atoms with no rehybridization of the outermost carbon edge atoms. Both zigzag and chiral edges show the presence of edge states.   

Tunable magnetism at graphene edges

Electron-electron interactions drive clean graphene zigzag edges to a ferromagnetic state, known as edge magnetism. In this state, the spin of specific one-dimensional electronic modes, that are localized at the edge (the so-called edge state), is fully polarized. I will discuss a mechanism by which the edge magnetism can be manipulated via electric fields. One possible realization of this mechanism is based on graphene/graphane interfaces. As the field strength is varied, the graphene edge undergoes two phase transitions: (1) from fully polarized edge magnetism to a ferromagnetic Luttinger liquid (fLL) and (2) from the fLL to an ordinary Luttinger liquid. The intermediate phase (fLL) is a realization of the unusual itinerant one-dimensional ferromagnet and is therefore in seeming contradiction with the Lieb-Mattis theorem, which forbids such one-dimensional magnetism. The resolution of this seeming contradiction is shortly discussed.   

Dynamics of Graphene Edges Interaction under Joule-heating

The edge physics of graphene plays an essential role in the electronic properties of nanometer scale graphene. Studying the Joule-heating of a graphene sample supported by an integrated TEM-STM instrument is an effective way to sharpen graphene edges, and therefore produce smooth graphene nanoribbons, which will be studied in this work. Through observation of the movement of graphene platelets heat-treated within a crystalline domain of graphene substrate underneath, we advance our understanding about the mechanism of edge reconstruction, edge-edge interaction, in addition to the graphene substrate interaction for single layer graphene.   

Structure, Stability and Electronic Properties of Graphene Edges on Co(0001)

We recently demonstrated the growth of epitaxial graphene flakes on Co(0001) surfaces [1]. Here we combine low-temperature scanning tunneling microscopy (STM) measurements and DFT calculations to study graphene edge stability and electronic properties, as resulting from the coupling with the substrate. Graphene edges display straight well-ordered structure with zigzag orientation. DFT calculations provide insights into their stability by comparing several edge morphologies with both armchair and zigzag orientation. Simulated images indicate that different edge structures can be clearly distinguished in topography at low bias. The calculated electronic properties for the low energy edge structures are consistent with the measured STS tunneling spectra, which show a prominent edge-localized peak at low bias. [1] D. Eom et al., Nano Lett. 9, 2844 (2009).   

Chemical versus Thermal Folding of Graphene Edges

Using molecular dynamics (MD) simulations, we have investigated the kinetics of the graphene edge folding process. The lower limit of the energy barrier is found to be $\sim $380 meV/{\AA} (or about 800 meV per edge atom) and $\sim $50 meV/{\AA} (or about 120 meV per edge atom) for folding the edges of intrinsic clean single-layer graphene (SLG) and double-layer graphene (DLG), respectively. However, the edge folding barriers can be substantially reduced by imbalanced chemical adsorption, such as of H atoms, on the two sides of graphene along the edges. Our studies indicate that thermal folding is not feasible at room temperature (RT) for clean SLG and DLG edges and is feasible at high temperature only for DLG edges, whereas chemical folding (with adsorbates) of both SLG and DLG edges can be spontaneous at RT. These findings suggest that the folded edge structures of suspended graphene observed in some experiments are possibly due to the presence of adsorbates at the edges.   

Edge effects in Zigzag Graphene Nanoribbons

Analytical and numerical results based on the tight binding model are presented for zigzag graphene nanoribbons with z1 and z12$_1$2 edges. We show the crucial importance of the symmetry of the two edges in determining the electronic structures of the system. Examples of significant band gap narrowings due to symmetry breaking are illustrated.   

Mapping edge-state wavefunctions in chiral graphene nanoribbons

The electronic behavior of graphene is readily tunable through nanoscale patterning. A particularly important structural motif is the nanoribbon (GNR), a narrow strip of graphene defined by its width, length, and edge properties. GNRs, due to quantum confinement and edge effects, have been predicted to exhibit many novel behaviors, such as tunable energy gaps and the presence of magnetic edge states. Here we report measurement of the local electronic structure of GNRs with highly ordered edges obtained by unzipping carbon nanotubes. Due to variation in the precursor nanotubes, this synthesis method generally produces single- or multi-layered nanoribbons with varying widths, lengths and chiralities. We have combined scanning tunneling microscopy (STM) and spectroscopy (STS) to simultaneously characterize the structural and electronic properties of these GNRs at the atomic scale. In particular, we observe 1D edge states that exhibit an energy gap that is dependent on nanoribbon width and the chirality. We have further spatially mapped patterns in the electronic local density of states associated with different GNR spectroscopic resonances. These patterns are compared with theoretical simulations.   

Effects of edge-potential on armchair graphene open boundary and nanoribbon

The physics for the edge state formation and gap opening at an armchair graphene open boundary and nanoribbon due to an edge potential are investigated. At an open boundary, the edge-potential $U_0 $ is shown to turn on pseudospin-fipped (intravalley) scattering even though $U_0 $ does not post an apparent breaking of the AB site (basis atoms) symmetry. The interference between the pseudospin conserving (intervalley) and nonconserving (intravalley) processes in the scattering state leads to a finite out-of-plane pseudospin density. Similar two-waves feature in the evanescent regime leads to the formation of the edge state. This physical origin of the edge state is different from that for the Tamm states in semiconductors. For an armchair graphene nanoribbon with gapless energy spectrum, applying $U_0 $ to both edges opens up an energy gap. In addition, dispersive edge state can be found inside the energy gap for the bulk-like states. The$U_0 $-induced out-of-plane pseudospin density vanishes for the armchair graphene nanoribbon, but we expect it to be finite, for more general cases, at an armchair graphene open boundary.   

Formation of unconventional standing waves at graphene edges

The electron scattering properties of graphene edge have been investigated by the interference images using the scanning tunneling microscopy (STM). A conventional metal with a terrace and a step can be modeled as a two-dimensional electron gas with a hard wall and this behavior was directly observed at the steps of Au(111) and Cu(111) surfaces by STM. Now, a question arises as to how two sublattices and two inequivalent valleys in graphene affect the scattering and the standing wave formation. We present how the contributions from two valleys vary in the scattering at different graphene edges. For the zigzag edge, only intravalley scattering is possible due to the different edge-direction crystal momentum of two valleys. For the armchair edge, in contrast, the wave is reflected mostly via intervalley scattering and as a result, an atomic-scale nodelike pattern and beats in the standing wave are generated near the edge. When the incident angle is small, this intervalley scattering process is quite robust in the presence of defects so that we can still observe nodal patterns even for edges of relatively high defect densities.