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.

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 .

Irradiation of graphene on SiO2 by 500 eV Ne and He ions creates defects that cause intervalley scattering as is evident from a significant Raman D band intensity. The defect scattering gives a conductivity proportional to charge carrier density, with mobility decreasing as the inverse of the ion dose. The mobility decrease is 4 times larger than for a similar concentration of singly charged impurities. The minimum conductivity decreases proportional to the mobility to values lower than 4e(2)/pih, the minimum theoretical value for graphene free of intervalley scattering. Defected graphene shows a diverging resistivity at low temperature, indicating insulating behavior. The results are best explained by ion-induced formation of lattice defects that result in midgap states.

Graphene is a model system for the study of electrons confined to a strictly two-dimensional layer 1 and a large number of electronic phenomena have been demonstrated in graphene, from the fractional 2,3 quantum Hall effect to superconductivity 4 . However, the coupling of conduction electrons to local magnetic moments 5,6 , a central problem of condensed-matter physics, has not been realized in graphene, and, given carbon's lack of d or f electrons, magnetism in graphene would seem unlikely. Nonetheless, magnetism in graphitic carbon in the absence of transition-metal elements has been reported 7-9 , with explanations ranging from lattice defects 10 to edge structures 11 to negative curvature regions of the graphene sheet 12 . Recent experiments suggest that correlated defects in highly-ordered pyrolytic graphite (HOPG), induced by proton irradiation 8 or native to grain boundaries 7 , can give rise to ferromagnetism. Here we show that point defects (vacancies) in graphene 13 are local moments which interact strongly with the conduction electrons through the Kondo effect 6,14-16 , providing strong evidence that defects in graphene are indeed magnetic. The Kondo temperature T K is tunable with carrier density from 30 to 90 K; the high T K is a direct consequence of strong coupling of defects to conduction electrons in a Dirac material 16 .We previously reported the resistivity of graphene with vacancies induced by ion irradiation in ultra-high vacuum (UHV; ref. 13). Here we present a detailed study of the gate voltage (V g ) and temperature (T ) dependence of the resistivity ρ(V g , T ) in similar graphene with vacancies over a wider temperature range 300 mK < T < 290 K. Apart from weak-localization (WL) corrections 17,18 , we find that ρ(V g ,T ) is explained by a temperatureindependent contribution ρ c (V g ) due to non-magnetic disorder plus a temperature-dependent contribution ρ K (V g ,T ), not present in as-prepared graphene 13 , which follows the universal temperature dependence expected for Kondo scattering from a localized 1/2-spin with a single scaling parameter T K .Graphene with vacancies is prepared as described in ref. 13. After irradiation, the devices were annealed overnight at 490 K in UHV, and then exposed to air during transfer to a 3 He samplein-vacuum cryostat. Figure 1a shows σ (V g ) measured at 17 K for a graphene device (sample Q6) before irradiation, immediately after irradiation, and measured at 300 mK after annealing and transfer to the 3 He cryostat. V g is applied to the Si substrate to tune the carrier density n = c g V g /e, where c g = 1.15×10 −8 F cm −2 is the gate capacitance, and e the elementary charge. The mobility of the device is approximately 4000, 300, and 2000 cm 2 V −1 s −1 , respectively, for these three measurements; the conductivity and mobility recover significantly after annealing and air exposure, consistent with our previous study 13 . From the post-annealing mobility we estimate that this device has a defect density, n imp , of approximately 3×10 11 cm −2 , alt...

We reduce the dimensionless interaction strength α in graphene by adding a water overlayer in ultra-high vacuum, thereby increasing dielectric screening. The mobility limited by long-range impurity scattering is increased over 30 percent, due to the background dielectric constant enhancement leading to reduced interaction of electrons with charged impurities. However, the carrier-densityindependent conductivity due to short range impurities is decreased by almost 40 percent, due to reduced screening of the impurity potential by conduction electrons. The minimum conductivity is nearly unchanged, due to canceling contributions from the electron/hole puddle density and longrange impurity mobility. Experimental data are compared with theoretical predictions with excellent agreement. PACS numbers:Most theoretical and experimental work on graphene has focused on its gapless, linear electronic energy dispersion E = v F k. One important consequence of this linear spectrum is that the dimensionless coupling constant α (or equivalently r s , defined here as the ratio between the graphene Coulomb potential energy and kinetic energy) is a carrier-density independent constant [1, 2], and as a result, the Coulomb potential of charged impurities in graphene is renormalized by screening, but strictly maintains its long-range character. Thus there is a clear dichotomy between long-range and short-range scattering in graphene, with the former giving rise to a conductivity linear [2,3] in carrier density (constant mobility), and the latter having a constant conductivity independent of carrier density. Charged impurity scattering necessarily dominates at low carrier density, and the minimum conductivity at charge neutrality is determined by the charged impurity scattering and the self-consistent electron and hole puddles of the screened impurity potential [3,4,5,6].Apart from the linear spectrum, an additional striking aspect of graphene, setting it apart from all other twodimensional electron systems, is that the electrons are confined to a plane of atomic thickness. This fact has a number of ramifications which are only beginning to be explored [7]. One such consequence is that graphene's properties may be tuned enormously by changing the surrounding environment. Here we provide a clear demonstration of this by reducing the dimensionless coupling constant α in graphene by more than 30 percent through the addition of a dielectric layer (ice) on top of the graphene sheet. Upon addition of the ice layer, the mobility limited by long-range scattering by charged impurities increases by 31 percent, while the conductivity limited by short-range scatterers decreases by 38 percent. The minimum conductivity value remains nearly unchanged. The FIG. 1:Schematic illustrating dielectric screening in graphene. The dielectric environment controls in the interaction strength parameterized by the coupling constant α.opposing effects of reducing α on short-and long-range scattering are easily understood theoretically. The major effect on long-range...

Grain boundaries are observed and characterized in chemical vapor deposition-grown sheets of hexagonal boron nitride (h-BN) via ultra-high-resolution transmission electron microscopy at elevated temperature. Five- and seven-fold defects are readily observed along the grain boundary. Dynamics of strained regions and grain boundary defects are resolved. The defect structures and the resulting out-of-plane warping are consistent with recent theoretical model predictions for grain boundaries in h-BN.

The experimental manifestation of topological effects in bulk materials under ambient conditions, especially those with practical applications, has attracted enormous research interest. Recent discovery of Weyl semimetal provides an ideal material platform for such endeavors. The Berry curvature in a Weyl semimetal becomes singular at the Weyl node, creating an effective magnetic monopole in the k-space. A pair of Weyl nodes carry quantized effective magnetic charges with opposite signs, and therefore, opposite chirality. Although Weyl-point-related signatures such as chiral anomaly and non-closing surface Fermi arcs have been detected through transport and ARPES measurements, direct experimental evidence of the effective k-space monopole of the Weyl nodes has so far been lacking. In this work, signatures of the singular topology in a type-II Weyl semimetal TaIrTe4 is revealed in the photo responses, which are shown to be directly related to the divergence of Berry curvature. As a result of the divergence of Berry curvature at the Weyl nodes, TaIrTe4 exhibits unusually large photo responsivity of 130.2 mA/W with 4-m excitation in an unbiased field effect transistor at room temperature arising from the third-order nonlinear optical response.The room temperature mid-IR responsivity is approaching the performance of commercial HgCdTe detector operating at low temperature, making Type-II Weyl semimetal TaIrTe4 of practical importance in terms of photo sensing and solar energy harvesting. Furthermore, the circularly polarized galvanic response is also enhanced at 4-m, possibly due to the same Berry curvature singularity enhancement as the shift current. Considering the optical selection rule of Weyl cones with opposite chirality, it may open new experimental possibilities for studying and controlling the chiral polarization of Weyl Fermions through an in-plane DC electric field in addition to the optical helicities.