We have achieved mobilities in excess of 200,000 cm 2 V −1 s −1 at electron densities of ∼2×10 11 cm −2 by suspending single layer graphene. Suspension ∼150 nm above a Si/SiO2 gate electrode and electrical contacts to the graphene was achieved by a combination of electron beam lithography and etching. The specimens were cleaned in situ by employing current-induced heating, directly resulting in a significant improvement of electrical transport. Concomitant with large mobility enhancement, the widths of the characteristic Dirac peaks are reduced by a factor of 10 compared to traditional, non-suspended devices. This advance should allow for accessing the intrinsic transport properties of graphene. Graphene, the latest addition to the family of twodimensional (2D) materials, is distinguished from its cousins by its unusual band structure, rendering the quasiparticles in it formally identical to massless, chiral fermions. The experimental realization of graphene thus presents tantalizing opportunities to study phenomena ranging from the topological phase resulting in exotic quantum Hall states [1,2] to the famous Klein paradox -the anomalous tunneling of relativistic particles [3]. However, despite tremendous interest and concerted experimental efforts , the presence of strong impurity scattering -which limits the electron mean free path to less than a micron -has been a major barrier to progress. At the same time, there is strong evidence that graphene is a nearly perfect crystal free of the structural defects [4,5] that characterize most conductors. As a result, it has been put forth that the scattering of charge carriers stems from extrinsic sources [7,8,9,10].Although the exact nature of the scattering that limits the mobility of graphene devices remains unclear, evidence has mounted that interactions with the underlying substrate are largely responsible. Surface charge traps [6,7,8,9], interfacial phonons [11], substrate stabilized ripples [5,10,12], and fabrication residues on or under the graphene sheet may all contribute. Consequently, improving substrate quality or eliminating the substrate altogether by suspending graphene over a trench seems a promising strategy towards higher quality samples. While devices suspended over the substrate were achieved in the past [12,13], they lacked multiple electrical contacts thus precluding transport measurements.In this Letter we report the fabrication of electrically contacted suspended graphene and achieve a tenfold improvement in mobility as compared to the best values reported in the literature for traditional devices fabricated on a substrate. Besides opening new avenues for studying the intrinsic physics of Dirac fermions, this improvement demonstrates the dominant role played by extrinsic scattering in limiting the transport properties of unsuspended graphene samples.The fabrication of a suspended graphene device starts with optically locating a single-layer mechanically exfoliated graphene flake on top of a silicon substrate covered with 300 nm of SiO 2 . Singl...

We report the influence of uniaxial tensile mechanical strain in the range 0-2.2% on the phonon spectra and bandstructures of monolayer and bilayer molybdenum disulfide (MoS2) two-dimensional crystals. First, we employ Raman spectroscopy to observe phonon softening with increased strain, breaking the degeneracy in the E' Raman mode of MoS2, and extract a Grüneisen parameter of ~1.06. Second, using photoluminescence spectroscopy we measure a decrease in the optical band gap of MoS2 that is approximately linear with strain, ~45 meV/% strain for monolayer MoS2 and ~120 meV/% strain for bilayer MoS2. Third, we observe a pronounced strain-induced decrease in the photoluminescence intensity of monolayer MoS2 that is indicative of the direct-to-indirect transition of the character of the optical band gap of this material at applied strain of ~1%. These observations constitute a demonstration of strain engineering the band structure in the emergent class of two-dimensional crystals, transition-metal dichalcogenides.

2The 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 4 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.Since its discovery in 2004 1 , graphene has attracted attention because of its unusual two dimensional (2D) structure and potential for applications [2][3][4] . Due to its exceptional mechanical properties 5 and low mass density, graphene is an ideal material for use in nanoelectromechanical systems (NEMS), which are of great interest both for fundamental studies of mechanics at the nanoscale and for a variety of applications, including force 6 , position 7 and mass 8 sensing. Recent studies using optical and scanned probe detection have shown that micron-size graphene flakes can act as MHz-range NEMS resonators 9,10 . Electrical readout of these devices is important for integration and attractive for many applications. In addition, characterization of the basic attributes of these devices, including their response to applied voltage, added mass, and changes 3 in temperature, allows detailed modeling of their behavior, which is crucial for rational device design.Samples are fabricated by first locating monolayer graphene flakes on Si/SiO 2 substrates, then patterning metal electrodes and etching away the SiO 2 to yield suspended graphene. The ability to choose monolayers in advance provides control of device properties and facilitates electrical readout. The fabrication method also provides control over the lateral dimensions; devices can be either micron-wide sheets (Fig. 1a) or lithographically defined nanoribbons (Fig.1b). Because the etchant diffuses freely under the sheets, the SiO 2 is removed at the same rate everywhere under the graphene, so that the distance between the substrate and the suspended sheet is constant (~100 nm) across each device. For the same reason, the portion of each electrode that contacts the graphene is also suspended 11,12 , as depicted in Fig. 1c.Following previous work 13-15 , we implemented an all-electrical high-frequency mixing approach ( Fig. 1d) and 5). In addition to being of fundamental interest as a coupled nanoscale-microscale system, these resonances demonstrate that grap...

The resistivity of ultra-clean suspended graphene is strongly temperature (T ) dependent for 5 K< T < 240 K. At T ∼ 5 K transport is near-ballistic in a device of ∼ 2 µm dimension and a mobility ∼ 170, 000 cm 2 /Vs. At large carrier density, n > 0.5×10 11 cm −2 , the resistivity increases with increasing T and is linear above 50 K, suggesting carrier scattering from acoustic phonons. At T = 240 K the mobility is ∼ 120, 000 cm 2 /Vs, higher than in any known semiconductor. At the charge neutral point we observe a non-universal conductivity that decreases with decreasing T , consistent with a density inhomogeneity <10 8 cm −2 .

When electrons are confined in two dimensions (2D) and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall (FQH) liquids 1 . In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions 2,3 . However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena 4,5 , despite concerted experimental efforts and intense theoretical interest 6-12 . Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields.In a perpendicular magnetic field, the energy spectrum of a clean two-dimensional electron system (2DES) splits into a fan of Landau levels (LLs). When the Fermi energy is tuned to lie between the LLs, the system enters the integer quantum Hall (IQH) regime, in which current is carried by states at the edge of the sample and the overall conductance is quantized as G=νe 2 /h, where ν is an integer Landau level filling factor. Already the first observation of the IQH effect in graphene demonstrated an unusual sequence of filling factors ν=±2,±6,±10..., which differs from previously studied 2DESs. This sequence originates from two peculiar features of graphene: the four-fold spin and pseudo-spin (valley) degeneracy of LLs and the existence of a non-trivial Berry phase associated with the pseudo-spin of Dirac quasiparticles 13 .In clean samples and under very strong magnetic fields, additional IQH states emerge at filling factors ν=0, ±1 4,5 . These fragile IQH states are conjectured to result from electron-electron (e-e) interactions lifting the pseudospin and spin degeneracy of the zeroth LL 14 . The nature of these states, and in particular the unusual ν=0 state, responsible for the divergent resistivity of graphene at high magnetic fields 15 , has raised considerable interest in the effect of e-e interactions among Dirac quasiparticles. In conventional semiconductor heterojunctions such correlation effects are spectacularly manifested in the FQH effect, where new electronic ground states are formed in which the elementary excitations are composite particles with fractional charge 16 . The possibility of a FQH effect in graphene, and t...

The conductivity of graphene samples with various levels of disorder is investigated for a set of specimens with mobility in the range of 1-20x10(3) cm2/V sec. Comparing the experimental data with the theoretical transport calculations based on charged impurity scattering, we estimate that the impurity concentration in the samples varies from 2-15x10(11) cm(-2). In the low carrier density limit, the conductivity exhibits values in the range of 2-12e2/h, which can be related to the residual density induced by the inhomogeneous charge distribution in the samples. The shape of the conductivity curves indicates that high mobility samples contain some short-range disorder whereas low mobility samples are dominated by long-range scatterers.

We report the use of atomically thin layers of graphene as a protective coating that inhibits corrosion of underlying metals. Here, we employ electrochemical methods to study the corrosion inhibition of copper and nickel by either growing graphene on these metals, or by mechanically transferring multilayer graphene onto them. Cyclic voltammetry measurements reveal that the graphene coating effectively suppresses metal oxidation and oxygen reduction. Electrochemical impedance spectroscopy measurements suggest that while graphene itself is not damaged, the metal under it is corroded at cracks in the graphene film. Finally, we use Tafel analysis to quantify the corrosion rates of samples with and without graphene coatings. These results indicate that copper films coated with graphene grown via chemical vapor deposition are corroded 7 times slower in an aerated Na(2)SO(4) solution as compared to the corrosion rate of bare copper. Tafel analysis reveals that nickel with a multilayer graphene film grown on it corrodes 20 times slower while nickel surfaces coated with four layers of mechanically transferred graphene corrode 4 times slower than bare nickel. These findings establish graphene as the thinnest known corrosion-protecting coating.

The optical response of semiconducting monolayer transition-metal dichalcogenides (TMDCs) is dominated by strongly bound excitons that are stable even at room temperature. However, substrate-related effects such as screening and disorder in currently available specimens mask many anticipated physical phenomena and limit device applications of TMDCs. Here, we demonstrate that that these undesirable effects are strongly suppressed in suspended devices. Extremely robust (photogain > 1,000) and fast (response time < 1 ms) photoresponse allow us to study, for the first time, the formation, binding energies, and dissociation mechanisms of excitons in TMDCs through photocurrent spectroscopy. By analyzing the spectral positions of peaks in the photocurrent and by comparing them with first-principles calculations, we obtain binding energies, band gaps and spin-orbit splitting in monolayer TMDCs. For monolayer MoS2, in particular, we obtain an extremely large binding energy for band-edge excitons, Ebind ≥ 570 meV. Along with band-edge excitons, we observe excitons associated with a van Hove singularity of rather unique nature. The analysis of the source-drain voltage dependence of photocurrent spectra reveals exciton dissociation and photoconversion mechanisms in TMDCs.