Comparison of graphene [(a)–(d)] and conventional 2D electron systems [(e)–(i)]. (a) Lattice structure and first BZ; (b) Dirac equations; (c) 3D (left) and 2D (right) energy dispersions; (d) DOS as a function of energy; (f) Schematic of a conventional 2DEG confined by electrostatic potentials in the direction; (g) Schrödinger equation; (h) dispersion curves; (i) DOS as a function of energy.
Hall conductivity and longitudinal resistivity of graphene as a function of carrier concentration at an applied magnetic of 14 T and temperature of 4 K. Pronounced QHE plateaus are observed at with the first plateau occurred at . Reprinted by permission from Macmillan Publishers Ltd: Nature, Novoselov et al., 438, 197 (2005), Copyright 2005.
Comparison of graphene and normal electron systems under an external magnetic field [(a) and (d)], in ribbon and wire form [(b) and (e)] and with a 1D potential barrier [(c) and (f)].
AFM images HOPG. [(c) and (d)] Are the high-magnification images of the portions indicated in (a) as C and D, respectively. Reprinted by permission from Macmillan Publishers Ltd, Nature, Hiura et al., 367, 148 (1994), Copyright 1994.
Scanning electron micrographs of (a) and (b) HOPG islands, and (c) and (d) HOPG plates on Si(001) substrates. Reprinted with permission from X. Lu et al., Nanotechnology 10, 269 (1999), Copyright 1999, IOP Publishing Ltd.
Graphene films obtained by mechanical exfoliation. (a) Photograph of a graphene flake with a thickness of 3 nm placed on top of an oxidized Si wafer. (b) AFM image of area of the flake in (a) near its edge (dark brown, surface; orange, 3 nm height above the surface). (c) AFM image of SLG (central area). (d) SEM image of a few layer graphene device (e) Schematic view of the device in (d). From Novoselov et al., Science 306, 666 (2004), Reprinted with permission from AAAS.
Raman spectra of pristine graphite (top), GO (middle), and the reduced GO (bottom). Reprinted from Stankovich et al., Carbon 45, 1558 (2007), Copyright 2007, with permission from Elsevier.
Scanning electron micrographs of (a) starting graphite, (b) after intercalation with potassium and exfoliation with ethanol, and (c) and (d) graphite nanoplatelets after further exfoliation induced by microwave radiation. The scale bars in Fig. 8(a)–8(d) are , , , and 273 nm, respectively. These figures are re-arranged from L. M. Viculis et al., Mater. Chem. 15, 974 (2005). Reproduced by permission of the Royal Society of Chemistry.
Chemically derived GNRs down to sub-10-nm width. (a) (Left) Photograph of a polymer PmPV/DCE solution with GNRs stably suspended in the solution. Right: schematic drawing of a GNR with two units of a PmPV polymer chain adsorbed on top of the graphene via stacking. (b) to (f) AFM images of selected GNRs with widths in the 50 nm, 30 nm, 20 nm, 10 nm and sub-10-nm regions, respectively. In (b), left ribbon height , one layer; middle ribbon height , two layers; right ribbon height , two layers. In (c), the three GNRs are two to three layers thick. In (d), ribbons are one (right image) to three layers. In (e), ribbons are two to three layers. In (f), the heights of the ultranarrow ribbons are , 1.4 nm, and 1.5 nm, respectively. All scale bars indicate 100 nm. From Li et al., Science 319, 1229 (2008). Reprinted with permission from AAAS.
(a) Atomically resolved images of the graphene overlayer on Ru(0001) surface. (b) Model shows a commensurate Ru structure with graphene unit cells. The first layer Ru atoms are the light gray spheres, the second layer Ru atoms dark gray, and the graphene layer is the honeycomb net. There is no rotation between the graphene and Ru lattices. Reprinted with permission from Marchini et al., Phys. Rev. B 76, 075429 (2007), Copyright 2007 by the American Physical Society.
(a) ARPES spectrum of clean Ir(111), . and represent the K points of Ir and graphene, respectively. are surface states. (b) ARPES spectrum of Ir(111) covered by graphene along the same azimuth as in (a). Horizontal arrows denote the minigap at the intersection of the primary Dirac cone and BZ boundary. is a replica band. [(c) and (d)] ARPES spectra for and , respectively. The dashed lines are calculated bands for the Dirac cone replicas due to the superstructure. Reprinted with permission from Pletikosić et al., Phys. Rev. Lett. 102, 056808 (2009). Copyright 2009 by the American Physical Society.
Process flowchart of synthesis and transfer of graphene from Ni to substrate. (a) Synthesis of patterned graphene films on thin nickel layers. (b) Etching using (or acids) and transfer of graphene films using a PDMS stamp. (c) Etching using buffered HF or hydrogen fluoride solution and transfer of graphene films. Reprinted by permission from Macmillan Publishers Ltd: Nature, Kim et al., 457, 706 (2009), Copyright 2009.
(a) AFM image of H-etched 6H–SiC(0001) surface; (b) AFM image of graphene on 6H–SiC(0001) with a nominal thickness of one monolayer formed by annealing in UHV at a temperature of about ; (c) LEEM image of a UHV-grown graphene film with a nominal thickness of 1.2 monolayer; light, medium, and dark gray correspond to a local thickness of zero monolayer, one monolayer, and two monolayer, respectively; (d) AFM image of graphene with a nominal thickness of 1.2 monolayer formed by annealing in ; (e) LEEM image of a sample equivalent to that of (d); (f) Close-up of the image shown in (e); (g) and (h) electron reflectivity spectra taken at the positions indicated by the lines in (f); (i) close-up AFM images of the film shown in (d). Reprinted by permission from Macmillan Publishers Ltd: Nature, Emtsev et al., 8, 203 (2009), Copyright 2009.
LL spectrum in epitaxial graphene. (a) Tunneling differential conductance spectra vs sample bias of LLs in MLG at (blue dot: experimental data; red line: fitting in Voigt line shape at LL peak positions). Inset shows the LL peak position vs square root of LL index and applied field from the peak positions in (a). Solid lines are fits to a bilayer model with interlayer coupling of zero (red), 150 meV (black), and 300 meV (blue). (b) LL spectra for various applied magnetic fields from 0 to 6 T. The curves are offset for clarity (tunneling set point, , ). (c) LL peak energies for applied fields of 1 to 8 T, showing a collapse of the data when plotted vs square root of LL index and applied field. The solid line shows a linear fit yielding a characteristic velocity of . Inset: the shift in the peak position as a function of applied field (symbols). The solid line is a linear fit to the data points. From Miller et al., Science 324, 924 (2009). Reprinted with permission from AAAS.
Schematic of MWPECVD used in Refs. 41, 42, 229, and 230.
SEM images of carbon nanostructures grown at different flow rate ratios. (a) 30, (b) 15, (c) 10, (d) 6, (e) 4, (f) 1. Scale bars: (a), (b), (d), and (f) , (c) and (e) 100 nm. Y. H. Wu et al., J. Mater. Chem. 14, 469 (2004). Reproduced by permission of the Royal Society of Chemistry.
SEM images of CNWs grown at a flow rate ratio of 4. Scale bars: (a) 100 nm and (b) . (a) Was taken at a tilt angle of 25°. Y. H. Wu et al., J. Mater. Chem. 14, 469 (2004). Reproduced by permission of the Royal Society of Chemistry.
HRTEM images of CNWs grown at a flow rate ratio of 4. Reprinted with permission from Yang, Ph.D. thesis, National University of Singapore, 2004.
Schematic of the growth model of carbon nanosheets. : electric field near a substrate surface; : carbon-bearing growth species impinging from gas phase; : growth species diffuse along carbon nanosheet surface; H: atomic hydrogen impinging from gas phase; : defects removed from carbon nanosheet by atomic hydrogen etching effects. Reprinted from Zhu et al., Carbon 45, 2229 (2007), Copyright 2007, with permission from Elsevier.
SEM images of CNW patterns formed by the electrical field of surface plasmons with different number of poles. (i) is the enlarged image of portion (a) in (h). Scale bars: . Adapted with permission from Wu et al., Nano. Lett. 2, 355 (2002). Copyright 2002, American Chemical Society.
(a) Emission current density as a function of the electrical field at different temperatures for CNWs and (b) the corresponding FN plots of the curves in (a). The inset of (a) shows the sample configuration for field emission measurement. Y. H. Wu et al., J. Mater. Chem. 14, 469 (2004). Reproduced by permission of the Royal Society of Chemistry.
(a) Flat graphene crystal in real space (perspective view). (b) The same for corrugated graphene. (c) The reciprocal space for a flat sheet is a set of rods (red) directed perpendicular to the reciprocal lattice of graphene (black hexagon). (d) For the corrugated sheet, a superposition of the diffracting beams from microscopic flat areas effectively turns the rods into cone-shaped volumes so that diffraction spots become blurred at large angles (indicated by the dotted lines) and the effect is more pronounced further away from the tilt axis. [(e) and (f)] Electron diffraction patterns from a graphene monolayer under incidence angles of 0° and 26°, respectively. The roughness of graphene could be measured from diffraction patterns obtained at different tilt angles. Reprinted by permission from Macmillan Publishers Ltd: Nature, Meyer et al., 446, 60 (2007), Copyright 2007.
(a) Raw HRTEM image of the edge of a graphene nanosheet showing a bilayer structure with Moire´ pattern. (b) Fast Fourier transform of Fig. 1(a) showing two sets of hexagons with 30° rotation between them. (c) Red and green hexagons overlaid on the FFT to indicate the two sets of spots. (d) Reconstructed image after filtering in the frequency domain to include contributions from both sets of hexagons. (e) Reconstructed image showing the back graphene layer with one set of hexagon spots removed by filtering in the frequency domain. Inset shows a magnified section of the graphene indicated with a red box. (f) Mask used to filter in the frequency domain to obtain panel (e), color region is used for the reconstructed image. (g) Mask used for the reconstructed image of the front graphene layer in panel (h). (h) Reconstructed image of the front graphene layer after filtering in the frequency domain. Adapted with permission from Warner et al., Nano Lett. 9, 102 (2009). Copyright 2009 American Chemical Society.
(a) HRTEM image of the Moire’ pattern produced in the bilayer structure observed in Fig. 4.2.2. (b) Structural representation of two graphene layers with 30° rotation. (c) Overlay of the structural representation in panel (b) with the HRTEM image in panel (a), showing excellent agreement with the areas of contrast. (d) Schematic diagram illustrating two graphene layers with 30° rotation added together to produce a superstructure. (e) HRTEM image of the superstructure illustrated in panel (d). (f) HRTEM image simulation of the superstructure illustrated in panel (d) and imaged in panel (e) showing excellent agreement. Adapted with permission from Warner et al., Nano Lett. 9, 102 (2009). Copyright 2009 American Chemical Society.
Bias-dependent topographic images show the progression from imaging the SiC interface structure at high bias to imaging the graphene overlayer at low bias. The tunneling current is fixed at 100 pA, and the bias voltages are (a) 1.0 V, (b) 0.5 V, (c) 0.25 V, (d) −1.0 V, (e) −0.5 V, and (f) −0.25 V. Red arrows indicate that different features [tetramers in (a), graphene maximum in (c), and trimers in (e)] are imaged at the same surface location, dependent on bias voltage. The white box in (a) designates the area magnified in Fig. 4.3.2(b). Reprinted with permission from Rutter et al., Phys. Rev. B 76, 235416 (2007). Copyright 2007 by the American Chemical Society.
Large area image of graphene topography and charge puddles. (a) constant current STM topography of graphene . (b) map taken simultaneously with (a) reveals electron puddles with a characteristic length of . Reprinted with permission from Macmillan Publishers Ltd: Nature, Zhang et al., 5, 722 (2009), Copyright 2009.
(a) Schematic geometry of possible Si adatom features consisting of one tetramer and hexagon. The three different colors (red, blue, and green) correspond to Si adatoms on three different sublattices as in (b). The gold atoms represent the Si atoms in the SiC substrate. (b) Magnified view of the first layer of graphene from Fig. 4.3.1(a). Three hexagons are observed to lie on the three different SiC sublattices, denoted by the three different colors. Tetramer features (yellow triangles) are what allow hexagons to switch to different sublattices. Reprinted with permission from Rutter et al., Phys. Rev. B 76, 235416 (2007). Copyright 2007 by the American Chemical Society.
(a) Raman spectra as a function of number of layers. (b) Zoom-in view of the Raman 2D band. (c) Raman image plotted by the intensity of G band. (d) The cross section of Raman image, which corresponds to the dash lines. Reprinted with permission from Ni et al., Nano Lett. 7, 2758 (2007). Copyright 2007 by the American Chemical Society.
(a) List of Raman spectra, showing G and (b) 2D peaks as a function of uniaxial strain. The incident light polarized along the strain direction, and no analyzer was used to collect the scattered signal. The numbers on the right side of the spectra are indicating the strain. Reprinted with permission from Mohiuddin et al., Phys. Rev. B 79, 205433 (2009). Copyright 2009 by the American Physical Society.
Raman spectra (left) and polar plot (right) of the and peak intensity as a function of the angle between the polarization direction of the incident light and the strain axis. The spectra were collected with an analyzer direction along the strain axis. The polar data are fitted to . Reprinted with permission from Mohiuddin et al., Phys. Rev. B 79, 205433 (2009). Copyright 2009 by the American Physical Society.
Raman spectra of epitaxial graphene grown on Si terminated SiC (Si–SiC) and C terminated SiC (C–SiC). Reprinted with permission from Ni et al., Phys. Rev. B 77, 115416 (2008). Copyright 2008 by the American Physical Society.
(a) Raman spectra at values of between −2.2 and . The dots are the experimental data, and the peaks are fitted by lorentzians. The Dirac point is indicated by the red line. (b) Peak position of the G band (top panel) and its FWHM (bottom panel) as a function of electron and hole doping. The predicted nonadiabatic trends (Ref. 342) are shown in solid blue lines. (c) Peak position of the 2D peak as a function of doping. The solid line is their adiabatic DFT calculation. Reprinted with permission from Macmillan Publishers Ltd: Nature, Das et al., 3, 210 (2008), Copyright 2008.
(a) Optical image of a SLG sheet contains folded (twisted) regions. (b) Schematically image of folded sample as shown in (a). The estimated twisted angle of top layer relative to the bottom layer is 12.3°. (c) Raman spectra of folded graphene from area Y when excited by 457, 488, and 532 nm laser. Raman imaging of the G band intensity of the graphene sample excited by 457 nm (d) and 488 nm (e) 532 nm lasers (f), respectively. As can be seen in (d), the G band intensity from area Y is much higher than that of SLG, which is times that of SLG. And this kind of enhanced G band intensity disappears when the excitation energy is 532 nm as shown in (f). The G band intensity from area Y is now the same as that of SLG. Therefore, there is a G band resonance for twisted bilayer graphene with rotation angle of under excitation energy of 457 nm (Ni et al., unpublished work).
Raman imaging results from edges with angles (a) 30°, (b) 60° (zigzag), (c) 90°, and (d) 60° (armchair). The positions and shapes of the SLG sheets can be seen from the images constructed by the G band intensity. The laser polarization is indicated by the green arrows. The superimposed frameworks are guides for the eye indicating the edge state. Note that the edge state of (b) and (d) were determined by the other pair of edges (not shown) with 30°/90° on the same piece of SLG. The scale bar is . Adapted from You et al. (Ref. 371).
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