Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation

Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality. Since its experimental discovery, graphene continues to attract enormous interest, in particular as a new kind of matter, in which electron transport is governed by a Dirac-like wave equation, and as a model system for studying electronic and phonon properties of other, more complex, graphitic materials[1-4]. Here, we uncover the constitutive relation of graphene and probe new physics of its optical phonons, by studying its Raman spectrum as a function of uniaxial strain. We find that the doubly degenerate E2g optical mode splits in two components, one polarized along the strain and the other perpendicular to it. This leads to the splitting of the G peak into two bands, which we call G+ and G-, by analogy with the effect of curvature on the nanotube G peak[5-7]. Both peaks red shift with increasing strain, and their splitting increases, in excellent agreement with first-principles calculations. Their relative intensities are found to depend on light polarization, which provides a useful tool to probe the graphene crystallographic orientation with respect to the strain. The singly degenerate 2D and 2D' bands also red shift, but do not split for small strains. We study the Gruneisen parameters for the phonons responsible for the G, D and D' peaks. These can be used to measure the amount of uniaxial or biaxial strain, providing a fundamental tool for nanoelectronics, where strain monitoring is of paramount importance[8, 9

Local Optical Probe of Motion and Stress in a multilayer graphene NEMS

Nanoelectromechanical systems (NEMSs) are emerging nanoscale elements at the crossroads between mechanics, optics and electronics, with significant potential for actuation and sensing applications. The reduction of dimensions compared to their micronic counterparts brings new effects including sensitivity to very low mass, resonant frequencies in the radiofrequency range, mechanical non-linearities and observation of quantum mechanical effects. An important issue of NEMS is the understanding of fundamental physical properties conditioning dissipation mechanisms, known to limit mechanical quality factors and to induce aging due to material degradation. There is a need for detection methods tailored for these systems which allow probing motion and stress at the nanometer scale. Here, we show a non-invasive local optical probe for the quantitative measurement of motion and stress within a multilayer graphene NEMS provided by a combination of Fizeau interferences, Raman spectroscopy and electrostatically actuated mirror. Interferometry provides a calibrated measurement of the motion, resulting from an actuation ranging from a quasi-static load up to the mechanical resonance while Raman spectroscopy allows a purely spectral detection of mechanical resonance at the nanoscale. Such spectroscopic detection reveals the coupling between a strained nano-resonator and the energy of an inelastically scattered photon, and thus offers a new approach for optomechanics

Performance of Monolayer Graphene Nanomechanical Resonators with Electrical Readout

The enormous stiffness and low density of graphene make it an ideal material for nanoelectromechanical (NEMS) applications. We demonstrate fabrication and electrical readout of monolayer graphene resonators, and test their response to changes in mass and temperature. The devices show resonances in the MHz range. The strong dependence of the resonant frequency on applied gate voltage can be fit to a membrane model, which yields the mass density and built-in strain. Upon removal and addition of mass, we observe changes in both the density and the strain, indicating that adsorbates impart tension to the graphene. Upon cooling, the frequency increases; the shift rate can be used to measure the unusual negative thermal expansion coefficient of graphene. The quality factor increases with decreasing temperature, reaching ~10,000 at 5 K. By establishing many of the basic attributes of monolayer graphene resonators, these studies lay the groundwork for applications, including high-sensitivity mass detectors

Aharonov-Bohm interferences from local deformations in graphene

One of the most interesting aspects of graphene is the tied relation between structural and electronic properties. The observation of ripples in the graphene samples both free standing and on a substrate has given rise to a very active investigation around the membrane-like properties of graphene and the origin of the ripples remains as one of the most interesting open problems in the system. The interplay of structural and electronic properties is successfully described by the modelling of curvature and elastic deformations by fictitious gauge fields that have become an ex- perimental reality after the suggestion that Landau levels can form associated to strain in graphene and the subsequent experimental confirmation. Here we propose a device to detect microstresses in graphene based on a scanning-tunneling-microscopy setup able to measure Aharonov-Bohm inter- ferences at the nanometer scale. The interferences to be observed in the local density of states are created by the fictitious magnetic field associated to elastic deformations of the sample.Comment: Some bugs fixe

Control and Characterization of Individual Grains and Grain Boundaries in Graphene Grown by Chemical Vapor Deposition

The strong interest in graphene has motivated the scalable production of high quality graphene and graphene devices. Since large-scale graphene films synthesized to date are typically polycrystalline, it is important to characterize and control grain boundaries, generally believed to degrade graphene quality. Here we study single-crystal graphene grains synthesized by ambient CVD on polycrystalline Cu, and show how individual boundaries between coalescing grains affect graphene's electronic properties. The graphene grains show no definite epitaxial relationship with the Cu substrate, and can cross Cu grain boundaries. The edges of these grains are found to be predominantly parallel to zigzag directions. We show that grain boundaries give a significant Raman "D" peak, impede electrical transport, and induce prominent weak localization indicative of intervalley scattering in graphene. Finally, we demonstrate an approach using pre-patterned growth seeds to control graphene nucleation, opening a route towards scalable fabrication of single-crystal graphene devices without grain boundaries.Comment: New version with additional data. Accepted by Nature Material

Etching and Narrowing of Graphene from the Edges

Large scale graphene electronics desires lithographic patterning of narrow graphene nanoribbons (GNRs) for device integration. However, conventional lithography can only reliably pattern ~20nm wide GNR arrays limited by lithography resolution, while sub-5nm GNRs are desirable for high on/off ratio field-effect transistors (FETs) at room temperature. Here, we devised a gas phase chemical approach to etch graphene from the edges without damaging its basal plane. The reaction involved high temperature oxidation of graphene in a slightly reducing environment to afford controlled etch rate (\leq ~1nm/min). We fabricated ~20-30nm wide GNR arrays lithographically, and used the gas phase etching chemistry to narrow the ribbons down to <10nm. For the first time, high on/off ratio up to ~10^4 was achieved at room temperature for FETs built with sub-5nm wide GNR semiconductors derived from lithographic patterning and narrowing. Our controlled etching method opens up a chemical way to control the size of various graphene nano-structures beyond the capability of top-down lithography.Comment: 18 pages, 4 figures, to appear in Nature Chemistr

Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering

Among many remarkable qualities of graphene, its electronic properties attract particular interest due to a massless chiral character of charge carriers, which leads to such unusual phenomena as metallic conductivity in the limit of no carriers and the half-integer quantum Hall effect (QHE) observable even at room temperature [1-3]. Because graphene is only one atom thick, it is also amenable to external influences including mechanical deformation. The latter offers a tempting prospect of controlling graphene's properties by strain and, recently, several reports have examined graphene under uniaxial deformation [4-8]. Although the strain can induce additional Raman features [7,8], no significant changes in graphene's band structure have been either observed or expected for realistic strains of approx. 10% [9-11]. Here we show that a designed strain aligned along three main crystallographic directions induces strong gauge fields [12-14] that effectively act as a uniform magnetic field exceeding 10 T. For a finite doping, the quantizing field results in an insulating bulk and a pair of countercirculating edge states, similar to the case of a topological insulator [15-20]. We suggest realistic ways of creating this quantum state and observing the pseudo-magnetic QHE. We also show that strained superlattices can be used to open significant energy gaps in graphene's electronic spectrum

Strain-engineered graphene grown on hexagonal boron nitride by molecular beam epitaxy

Graphene grown by high temperature molecular beam epitaxy on hexagonal boron nitride (hBN) forms continuous domains with dimensions of order 20 μm, and exhibits moiré patterns with large periodicities, up to ~30 nm, indicating that the layers are highly strained. Topological defects in the moiré patterns are observed and attributed to the relaxation of graphene islands which nucleate at different sites and subsequently coalesce. In addition, cracks are formed leading to strain relaxation, highly anisotropic strain fields, and abrupt boundaries between regions with different moiré periods. These cracks can also be formed by modification of the layers with a local probe resulting in the contraction and physical displacement of graphene layers. The Raman spectra of regions with a large moiré period reveal split and shifted G and 2D peaks confirming the presence of strain. Our work demonstrates a new approach to the growth of epitaxial graphene and a means of generating and modifying strain in graphene

Micro-Raman and micro-transmission imaging of epitaxial graphene grown on the Si and C faces of 6H-SiC

Micro-Raman and micro-transmission imaging experiments have been done on epitaxial graphene grown on the C- and Si-faces of on-axis 6H-SiC substrates. On the C-face it is shown that the SiC sublimation process results in the growth of long and isolated graphene ribbons (up to 600 μm) that are strain-relaxed and lightly p-type doped. In this case, combining the results of micro-Raman spectroscopy with micro-transmission measurements, we were able to ascertain that uniform monolayer ribbons were grown and found also Bernal stacked and misoriented bilayer ribbons. On the Si-face, the situation is completely different. A full graphene coverage of the SiC surface is achieved but anisotropic growth still occurs, because of the step-bunched SiC surface reconstruction. While in the middle of reconstructed terraces thin graphene stacks (up to 5 layers) are grown, thicker graphene stripes appear at step edges. In both the cases, the strong interaction between the graphene layers and the underlying SiC substrate induces a high compressive thermal strain and n-type doping

First-Principles Study of the Electronic and Magnetic Properties of Defects in Carbon Nanostructures

Understanding the magnetic properties of graphenic nanostructures is instrumental in future spintronics applications. These magnetic properties are known to depend crucially on the presence of defects. Here we review our recent theoretical studies using density functional calculations on two types of defects in carbon nanostructures: Substitutional doping with transition metals, and sp$^3$-type defects created by covalent functionalization with organic and inorganic molecules. We focus on such defects because they can be used to create and control magnetism in graphene-based materials. Our main results are summarized as follows: i)Substitutional metal impurities are fully understood using a model based on the hybridization between the $d$ states of the metal atom and the defect levels associated with an unreconstructed D$_{3h}$ carbon vacancy. We identify three different regimes, associated with the occupation of distinct hybridization levels, which determine the magnetic properties obtained with this type of doping; ii) A spin moment of 1.0 $\mu_B$ is always induced by chemical functionalization when a molecule chemisorbs on a graphene layer via a single C-C (or other weakly polar) covalent bond. The magnetic coupling between adsorbates shows a key dependence on the sublattice adsorption site. This effect is similar to that of H adsorption, however, with universal character; iii) The spin moment of substitutional metal impurities can be controlled using strain. In particular, we show that although Ni substitutionals are non-magnetic in flat and unstrained graphene, the magnetism of these defects can be activated by applying either uniaxial strain or curvature to the graphene layer. All these results provide key information about formation and control of defect-induced magnetism in graphene and related materials.Comment: 40 pages, 17 Figures, 62 References; Chapter 2 in Topological Modelling of Nanostructures and Extended Systems (2013) - Springer, edited by A. R. Ashrafi, F. Cataldo, A. Iranmanesh, and O. Or