The structure of suspended graphene sheets
arXiv:cond-mat/0701379 · doi:10.1038/nature05545
Abstract
The recent discovery of graphene has sparked significant interest, which has so far been focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particle. However, the structure of graphene - a single layer of carbon atoms densely packed in a honeycomb crystal lattice - is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional (2D) material and exhibits such a high crystal quality that electrons can travel submicron distances without scattering. On the other hand, perfect 2D crystals cannot exist in the free state, according to both theory and experiment. This is often reconciled by the fact that all graphene structures studied so far were an integral part of larger 3D structures, either supported by a bulk substrate or embedded in a 3D matrix. Here we report individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick and still display a long-range crystalline order. However, our studies by transmission electron microscopy (TEM) have revealed that suspended graphene sheets are not perfectly flat but exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically-thin single-crystal membranes offer an ample scope for fundamental research and new technologies whereas the observed corrugations in the third dimension may shed light on subtle reasons behind the stability of 2D crystals.
14 pages, includes supplementary information
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Cited by in corpus (574)
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- Theory of liquid film growth and wetting instabilities on graphene
- Quantum efficiency enhancement of bialkali photocathodes by an atomically thin layer on substrates
- Localized and quasi-localized energy levels in the electron spectrum of graphene with isolated boron and nitrogen substitutions
- Thermo-electromechanical effects in relaxed shape graphene and bandstructures of graphene quantum dots
- Graphene ground states
- All-optical control of topological valley transport in graphene metasurfaces
- Friction and mobility of carbon nanoparticles on a graphene sheet
- Weak antilocalization and Shubnikov-de Haas oscillations in CaCuSb single crystal
- Distribution of ripples in graphene membrane
- Comparative image simulations for phase-plate transmission electron microscopy
- A Perspective on Collective Properties of Atoms on 2D Materials
- Spontaneous symmetry breaking and the flat phase of crystalline membranes
- Effect of doping on the electronic properties of Graphene and T-graphene : A theoretical approach
- Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions
- Rippling of two-dimensional materials by line defects
- Magnetic Phases in Periodically Rippled Graphene
- Dirac Fermions in Inhomogeneous Magnetic Field
- Path-integral simulation of graphene monolayers under tensile stress
- Landau level broadening in graphene with long-range disorder -- Robustness of the n=0 level
- A numerical study of the rippling instability driven by electron-phonon coupling in graphene
- Edge state in AB-stacked bilayer graphene and its correspondence with SSH ladder
- Time-lapsed graphene moiré superlattice on Cu(111)
- Raman Spectroscopy of Graphene under Uniaxial Stress: Phonon Softening and Determination of the Crystallographic Orientation
- The morphology and interface structure of titanium on graphene
- Kirigami-Inspired Thermal Regulator
- Highly stable electronic properties of rippled antimonene under compressive deformation
- Strain-induced superfluid transition for atoms on graphene
- Isotopic effects in structural properties of graphene
- Limits of Lateral Expansion in Two-Dimensional Materials with Line Defects
- Properties of heavy rare-gases adlayers on graphene substrates
- Flexural phonons in supported graphene: from pinning to localization
- Topological Transition of Graphene from Quantum Hall Metal to Quantum Hall Insulator at
- Thermal control of graphene morphology: a signature of its intrinsic surface tension
- Spatial mapping of the Dirac point in monolayer and bilayer graphene
- Spin Transport in Armchair Silicene Nanoribbon on the Substrate: The Role of Charged Impurity
- Supercurrent and phase slips in a ballistic carbon nanotube embedded into a van der Waals heterostructure
- Single-molecule electron diffraction imaging with charge replacement
- Lindemann Parameters for solid Membranes focused on Carbon Nanotubes
- Autocorrected Off-axis Holography of 2D Materials
- Radiative decay effects influence the local electromagnetic response of the monolayer graphene with surface corrugations in terahertz range
- Bound states of charges on top of graphene in magnetic field
- Van der Waals Epitaxy on Freestanding Monolayer Graphene Membrane by MBE
- The orientation of CO intercalated between graphene and Ru(0001)
- Broad frequency and amplitude control of vibration in freestanding graphene via scanning tunneling microscopy with calculated dynamic pseudo-magnetic fields
- Thermally driven elastic membranes are quasi-linear across all scales
- Graphene Induced Large Shift of Surface Plasmon Resonances of Gold Films: Effective Medium Theory for Atomically Thin Materials
- Edge states in a honeycomb lattice: effects of anisotropic hopping and mixed edges
- Dynamics of Fluctuating Thin Sheets Under Random Forcing
- The Structure of Fluctuating Thin Sheets Under Random Forcing
- On corrected formula for graphene quantum conductivity
- Tuning near-gap electronic structure, interface charge transfer and visible light response of hybrid doped graphene and Ag3PO4 composite: Dopant effects
- Wide field of view crystal orientation mapping of layered materials
- Bending mode fluctuations and structural stability of graphene nanoribbons
- Formation of carbon nano and micro structures on C1+ irradiated copper surfaces
- Spontaneous crumpling of active spherical shells
- Koshino-Taylor effect in graphene
- Induced fractional valley number in graphene with topological defects
- Polarization amplification by spin-doping in nanomagnetic/graphene hybrid systems
- Does the Round Sphere Maximize the Free Energy of (2+1)-Dimensional QFTs?
- Elastic properties of moiré lattices in epitaxial two-dimensional materials
- Reduction of Interlayer Interaction in Multilayer Stacking Graphene with Carbon Nanotube Insertion: Insights from Experiment and Simulation
- Graphene Nanotechnology for the Next Generation Nonvolatile Memory
- Large-scale critical behavior of the rippling phase transition for graphene membranes
- Magnetic adatoms in two and four terminal graphene nanoribbons: A comparison between their spin polarized transport
- Low-energy quantum scattering induced by graphene ripples
- Direct Growth Graphene on Cu Nanoparticles by Chemical Vapor Deposition as Surface-Enhanced Raman Scattering Substrate for Label-Free Detection of Adenosine
- Graphene as a quantum surface with curvature-strain preserving dynamics
- Electronic structure and optical properties of Graphene Monoxide
- Geometrical properties of strained and twisted moiré heterostructures
- Apparent rippling with honeycomb symmetry and tunable periodicity observed by scanning tunneling microscopy on suspended graphene
- Universal wrinkling of freestanding atomically thin films
- Correlating 3D atomic defects and electronic properties of 2D materials with picometer precision
- Modelling two-dimensional Crystals with Defects under Stress: Superelongation of Carbon Nanotubes at high Temperatures
- Strain-Fluctuation-Induced Near-Quantization of Valley Hall Conductivity in Graphene Systems
- Self-Folding and Self-Scrolling Mechanisms of Edge-Deformed Graphene Sheets: A Molecular Dynamics Study
- The influence of Gaussian strain on sublattice selectivity of impurities in graphene
- Near-field radiative heat transfer and van der Waals friction between closely spaced graphene and amorphous SiO
- Fast hydrogen atom diffraction through monocrystalline graphene
- Dirac charge dynamics in graphene by infrared spectroscopy
- Probing divacancy defects in a zigzag graphene nanoribbon through RKKY exchange interaction
- Welding few-layered graphene ribbon via penetration of high-speed fullerenes
- Generation of Multiple Dirac Cones in Graphene under Double-periodic and Quasiperiodic Potentials
- Surface corrugations influence on monolayer graphene electromagnetic response
- Stability of zero-mode Landau levels in bilayer graphene against disorder in the presence of the trigonal warping
- New stable two dimensional silicon carbide nanosheets
- Solitons and spin transport in graphene boundary
- Spontaneous charge-ordered state in Bernal-stacked bilayer graphene
- Upper limit of spin relaxation in suspended graphene
- Electron Energy Loss Spectroscopy of 2D Materials in a Scanning Electron Microscope
- Self-Organized Platinum Nanoparticles on Freestanding Graphene
- Geometrically-induced localization of flexural waves on thin warped physical membranes
- Buckling in a rotationally invariant spin-elastic model
- Corrugation induced stacking solitons with topologically confined states in gapped bilayer graphene
- RKKY interaction on curved surfaces: Different behavior of Dirac and Schrödinger carriers as interaction mediating particles
- Nature of Spontaneous Curvature in Suspended Graphene
- Are Graphene Sheets Stable?
- Potential-driven eddy current in rippled graphene nanoribbons
- Van-Hove tuning of Fermi surface instabilities through compensated metallicity
- Ultraclean suspended graphene by radiolysis of adsorbed water
- Quantum friction and graphene
- Weak Localization and Antilocalization in Twisted Bilayer Graphene
- Nanoantenna properties of graphene membrane. Quantum theory
- Manipulating the fully spin-polarized edge currents in graphene ribbon
- Elastic Constants and Bending Rigidities from Long-Wavelength Perturbation Expansions
- Height correlation of rippled graphene and Lundeberg-Folk formula for magnetoresistance
- Quantum Buckling
- Physical Properties of the Spin Hamiltonian on Honeycomb Lattice Samples with Kekulé and Vacuum Polarization Corrections
- A simple transcendental travelling wave solution and stability study for the thermophoretic motion with variable heat transmission factors on substrate-supported grapheme sheet
- Quasi-freestanding monolayer heterostructure of graphene and hexagonal boron nitride on Ir(111) with a chiral boundary
- Landau levels in wrinkled and rippled graphene sheets
- Raman spectroscopy and imaging of graphene
- New Losses Mechanism in Graphene Nanoresonators due to the Synthetic Electric Fields caused by Inherent Out-of-Plain Membrane Corrugations
- Charge Transfer Properties Through Graphene Layers in Gas Detectors
- Simple correction to bandgap in IV and III-V semiconductors: an improved first-principles local density functional theory
- Graphene and Some of its Structural Analogues: Full-potential Density Functional Theory Calculations
- Melting and Rippling Phenomenan in Two Dimensional Crystals with localized bonding
- Geometry and dynamics of spring networks of spherical topology
- Sublattice polarization and filamentary superconductivity in strained graphene
- Deep Learning Segmentation of Complex Features in Atomic-Resolution Phase Contrast Transmission Electron Microscopy Images
- Second-order Overtone and Combinational Raman Modes of Graphene Layers in the Range of 1690 cm-1 to 2150 cm-1
- Disentangling morphology and conductance in amorphous graphene
- Strong magnetoresistance in a graphene Corbino disk at low magnetic fields
- Effect of Interlayer Shear to Graphene Resonators
- Clar Sextet Analysis of Triangular, Rectangular and Honeycomb Graphene Antidot Lattices
- Electronic states in a bilayer graphene quantum ripple
- Geometrical dynamics of edge-driven surface growth