The linear dispersion relation in graphene gives rise to a surprising prediction: the resistivity due to isotropic scatterers, such as white-noise disorder or phonons, is independent of carrier density, n. Here we show that electron-acoustic phonon scattering is indeed independent of n, and contributes only 30 Omega to graphene's room-temperature resistivity. At a technologically relevant carrier density of 1 x1012 cm-2, we infer a mean free path for electron-acoustic phonon scattering of >2 microm and an intrinsic mobility limit of 2 x 105 cm2 V-1 s-1. If realized, this mobility would exceed that of InSb, the inorganic semiconductor with the highest known mobility ( approximately 7.7 x 104 cm2 V-1 s-1; ref. 9) and that of semiconducting carbon nanotubes ( approximately 1 x 105 cm2 V-1 s-1; ref. 10). A strongly temperature-dependent resistivity contribution is observed above approximately 200 K (ref. 8); its magnitude, temperature dependence and carrier-density dependence are consistent with extrinsic scattering by surface phonons at the SiO2 substrate and limit the room-temperature mobility to approximately 4 x 104 cm2 V-1 s-1, indicating the importance of substrate choice for graphene devices.

The electronic properties of single-walled carbon nanotubes are shown here to be extremely sensitive to the chemical environment. Exposure to air or oxygen dramatically influences the nanotubes' electrical resistance, thermoelectric power, and local density of states, as determined by transport measurements and scanning tunneling spectroscopy. These electronic parameters can be reversibly "tuned" by surprisingly small concentrations of adsorbed gases, and an apparently semiconducting nanotube can be converted into an apparent metal through such exposure. These results, although demonstrating that nanotubes could find use as sensitive chemical gas sensors, likewise indicate that many supposedly intrinsic properties measured on as-prepared nanotubes may be severely compromised by extrinsic air exposure effects.

Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. When subject to both a magnetic field and a periodic electrostatic potential, two-dimensional systems of electrons exhibit a self-similar recursive energy spectrum. Known as Hofstadter's butterfly, this complex spectrum results from an interplay between the characteristic lengths associated with the two quantizing fields, and is one of the first quantum fractals discovered in physics. In the decades since its prediction, experimental attempts to study this effect have been limited by difficulties in reconciling the two length scales. Typical atomic lattices (with periodicities of less than one nanometre) require unfeasibly large magnetic fields to reach the commensurability condition, and in artificially engineered structures (with periodicities greater than about 100 nanometres) the corresponding fields are too small to overcome disorder completely. Here we demonstrate that moiré superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a periodic modulation with ideal length scales of the order of ten nanometres, enabling unprecedented experimental access to the fractal spectrum. We confirm that quantum Hall features associated with the fractal gaps are described by two integer topological quantum numbers, and report evidence of their recursive structure. Observation of a Hofstadter spectrum in bilayer graphene means that it is possible to investigate emergent behaviour within a fractal energy landscape in a system with tunable internal degrees of freedom.

We employ scanning probe microscopy to reveal atomic structures and nanoscale morphology of graphene-based electronic devices (i.e., a graphene sheet supported by an insulating silicon dioxide substrate) for the first time. Atomic resolution scanning tunneling microscopy images reveal the presence of a strong spatially dependent perturbation, which breaks the hexagonal lattice symmetry of the graphitic lattice. Structural corrugations of the graphene sheet partially conform to the underlying silicon oxide substrate. These effects are obscured or modified on graphene devices processed with normal lithographic methods, as they are covered with a layer of photoresist residue. We enable our experiments by a novel cleaning process to produce atomically clean graphene sheets.

These authors contributed equally to this work. Since the experimental realization of graphene 1 , extensive theoretical work has focused on short-range disorder 2-5 , "ripples" 6, 7 , or charged impurities 2, 3, 8-13 to explain the conductivity as a function of carrier density σ(n)[1,14-18], and its minimum value σ min near twice the conductance quantum 4e 2 /h[14, 15, 19, 20]. Here we vary the density of charged impurities n imp on clean graphene 21 by deposition of potassium in ultra high vacuum. At non-zero carrier density, charged impurity scattering produces the ubiquitously observed 1, 14-18 linear σ(n) with the theoretically-predicted magnitude. The predicted asymmetry 11 for attractive vs. repulsive scattering of Dirac fermions is observed. σ min occurs not at the carrier density which neutralizes n imp , but rather the carrier density at which the average impurity potential is zero 10 . σ min decreases initially with n imp , reaching a minimum near 4e 2 /h at non-zero n imp , indicating that σ min in present experimental samples does not probe Dirac-point physics 14, 15, 19, 20 but rather carrier density inhomogeneity due to the impurity potential 3, 9, 10 .

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We have observed new combination modes in the range from 1650 -2300 cm -1 in single-(SLG), bi-, few-layer and incommensurate bilayer graphene (IBLG) on silicon dioxide substrates. The M band at ~1750 cm -1 is suppressed for both SLG and IBLG. A peak at ~1860 cm -1 (iTALO -) is observed due to a combination of the iTA and LO phonons. The s with increasing number of layers and this peak is absent intensity of this peak decrease