In an ideal graphene sheet, charge carriers behave as two-dimensional Dirac fermions 1 . This has been confirmed by the discovery of a half-integer quantum Hall effect in graphene flakes placed on a SiO 2 substrate. The Dirac fermions in graphene, however, are subject to microscopic perturbations that include topographic corrugations and electron-density inhomogeneities (that is, charge puddles). Such perturbations profoundly alter Dirac-fermion behaviour, with implications for their fundamental physics as well as for future graphene device applications. Here we report a new technique of Diracpoint mapping that we have used to determine the origin of charge inhomogeneities in graphene. We find that fluctuations in graphene charge density are caused not by topographical corrugations, but rather by charge-donating impurities below the graphene. These impurities induce surprising standing wave patterns due to unexpected backscattering of Dirac fermions. Such wave patterns can be continuously modulated by electric gating. Our observations provide new insight into impurity scattering of Dirac fermions and the microscopic mechanisms limiting electronic mobility in graphene.Topographic corrugations and charge puddles in graphene are two of the most significant types of disorder in this new material. Topographic corrugations 2-4 , for example, have been suggested as a cause for the suppression of anticipated antilocalization 5 . Electron and hole puddles 6 have similarly been blamed for obscuring universal conductivity in graphene 7 . These issues are part of a puzzle regarding the factors that limit graphene's mobility [8][9][10][11][12] . In order for graphene to fulfil its promise as a next-generation nanodevice substrate it is important to understand the origin of the disorder and the influence it has on Dirac fermions. We have made new progress in this direction by using the techniques of scanning tunnelling microscopy (STM) and spectroscopy to simultaneously probe topographic and electronic disorder in graphene with an electron-density spatial resolution two orders of magnitude higher than previous scanning single-electron transistor microscopy measurements 6 . Figure 1a shows the STM topography of a typical 30 × 30 nm 2 area of a graphene monolayer on SiO 2 . We observe random corrugations with lateral dimension of a few nanometres and a vertical dimension of ∼1.5 Å (r.m.s.), probably due to roughness in the underlying SiO 2 surface and/or intrinsic ripples of the graphene sheet [2][3][4]13 . STM imaging at the atomic scale clearly resolves the graphene honeycomb lattice on top of the broader surface corrugation all over the sample surface (inset).We explored the inhomogeneous graphene charge density by spatially mapping the Dirac point (that is, the charge neutral point in the density of states of undoped graphene). The graphene local density of states at the Dirac point shows a local minimum, which is reflected by a dip in the tunnelling spectra of graphene (Fig. 1b) the loss of energy experienced by electrons ...

The use of boron nitride (BN) as a substrate for graphene nanodevices has attracted much interest since the recent report that BN greatly improves the mobility of charge carriers in graphene compared to standard SiO(2) substrates. We have explored the local microscopic properties of graphene on a BN substrate using scanning tunneling microscopy. We find that BN substrates result in extraordinarily flat graphene layers that display microscopic Moiré patterns arising from the relative orientation of the graphene and BN lattices. Gate-dependent dI/dV spectra of graphene on BN exhibit spectroscopic features that are sharper than those obtained for graphene on SiO(2). We observe a significant reduction in local microscopic charge inhomogeneity for graphene on BN compared to graphene on SiO(2).

The honeycomb lattice of graphene is a unique two-dimensional system where the quantum mechanics of electrons is equivalent to that of relativistic Dirac fermions 1,2 . Novel nanometre-scale behaviour in this material, including electronic scattering 3,4 , spin-based phenomena 5 and collective excitations 6 , is predicted to be sensitive to charge-carrier density. To probe local, carrier-density-dependent properties in graphene, we have carried out atomically resolved scanning tunnelling spectroscopy measurements on mechanically cleaved graphene flake devices equipped with tunable back-gate electrodes. We observe an unexpected gap-like feature in the graphene tunnelling spectrum that remains pinned to the Fermi level (E F ) regardless of graphene electron density. This gap is found to arise from a suppression of electronic tunnelling to graphene states near E F and a simultaneous giant enhancement of electronic tunnelling at higher energies due to a phonon-mediated inelastic channel. Phonons thus act as a 'floodgate' that controls the flow of tunnelling electrons in graphene. This work reveals important new tunnelling processes in gate-tunable graphitic layers.Graphene provides an ideal platform for the local study of high-mobility two-dimensional (2D) electrons because it can be fabricated on top of an insulating substrate. The availability of a back-gate electrode makes graphene the first gate-tunable 2D system directly accessible to scanning probe measurement (Fig. 1a). Previous experiments have demonstrated the power of scanning tunnelling microscopy (STM) to probe the local electronic structure of graphene grown epitaxially on SiC (refs 7-9). That system, however, cannot be easily gated, and questions remain as to the influence of the SiC substrate on the graphene layer 6,10 . Mechanically cleaved graphene is a desirable alternative to graphene grown on SiC because it can be readily gated and placed on wellcontrolled substrates (Fig. 1a), thus making it useful for extracting intrinsic graphene properties.The STM topography of a gated graphene flake device is shown in Fig. 2a. Corrugations with a lateral dimension of a few nanometres and a vertical dimension of ∼1.5Å (r.m.s. value over a 60 × 60 nm 2 area) are observed, probably due to roughness in the underlying SiO 2 (refs 11,12). The graphene honeycomb lattice can be clearly resolved on top of the surface corrugation, as seen more clearly in Fig. 2b. We explored the local electronic structure of these graphene flake devices using dI /dV measurements at zero gate voltage, as shown in Fig. 2c. Strikingly, the spectrum shows a ∼130 mV gap-like feature centred at the Fermi energy, E F , as opposed to the linear density of states that might be expected from elastic tunnelling to a Dirac cone. A local minimum in the tunnelling conductance spectrum can also be seen at V D = −138 mV, making the spectrum asymmetric about E F . Close examination of the low-bias spectrum (Fig. 2c, inset) reveals that the tunnelling conductance does not go to absolute zero in the gap...

Approximating the Fermi Level PositionIn order to determine the Fermi level position of our devices, we first measured the resistance vs.applied gate voltage dependence of the graphene sheet that contained the nanoresonators, as shown in Fig. S1. From these measurements we were able to determine the charge neutral point (CNP) for each device, which corresponds to applied gate voltage that aligns the Fermi level of the graphene with the Dirac point, leading to a peak in the resistance curve. Once the CNP was known, we used a simple capacitor model in order to approximate the position of E F for a given gate voltage. For a 285nm SiO 2 layer, this relationship is given by ‫ܧ|‬ ி | ൌ 0.0319ඥ|ܸ ே െ ܸ ீ |.For most devices, V G could be varied from -100V to +200V without causing electric breakdown of the SiO 2 layer.We found that our as-prepared samples were hole doped, and that the degree of hole doping was dependent on the etchant we used to remove the copper foil that the graphene was grown on. As shown in Fig. S1, when an Ammonium Persulfate (APS) solution (2% by wt.) was used as the etchant, the CNP typically occurred near V G =50V. In contrast, when an Iron(III) Chloride (FeCl) solution (40% by wt.) was used as the etchant, the CNP occurred at much higher gate biases, typically with V G near +180V. This intrinsic hole doping allowed us to electrostatically shift the E F from 0 to -0.52 eV.The above analysis applies to the bare graphene surface. However, it has been recently observed by Thongrattanasiri, et al 1 that the simple capacitance model typically used to estimate the Fermi level position of graphene devices may change when the graphene is patterned in a nanoribbon geometry. In particular, it was predicted by those authors that the Fermi level position can deviate strongly near the nanoribbon edges, and that this deviation can affect the plasmonic

Relativistic quantum mechanics predicts that when the charge of a superheavy atomic nucleus surpasses a certain threshold, the resulting strong Coulomb field causes an unusual atomic collapse state; this state exhibits an electron wave function component that falls toward the nucleus, as well as a positron component that escapes to infinity. In graphene, where charge carriers behave as massless relativistic particles, it has been predicted that highly charged impurities should exhibit resonances corresponding to these atomic collapse states. We have observed the formation of such resonances around artificial nuclei (clusters of charged calcium dimers) fabricated on gated graphene devices via atomic manipulation with a scanning tunneling microscope. The energy and spatial dependence of the atomic collapse state measured with scanning tunneling microscopy revealed unexpected behavior when occupied by electrons.

Infrared transmission measurements reveal the hybridization of graphene plasmons and the phonons in a monolayer hexagonal boron nitride (h-BN) sheet. Frequencywavevector dispersion relations of the electromagnetically coupled graphene plasmon/h-BN phonon modes are derived from measurement of nanoresonators with widths varying from 30 to 300 nm. It is shown that the graphene plasmon mode is split into two distinct optical modes that display an anticrossing behavior near the energy of the h-BN optical phonon at 1370 cm −1 . We explain this behavior as a classical electromagnetic strong-coupling with the highly confined near fields of the graphene plasmons allowing for hybridization with the phonons of the atomically thin h-BN layer to create two clearly separated new surface-phonon-plasmon-polariton (SPPP) modes.

We present a scanning tunneling spectroscopy (STS) study of the local electronic structure of single and bilayer graphene grown epitaxially on a SiC(0001) surface. Low voltage topographic images reveal fine, atomic-scale carbon networks, whereas higher bias images are dominated by emergent spatially inhomogeneous large-scale structure similar to a carbon-rich reconstruction of SiC(0001). STS spectroscopy shows a ~100meV gap-like feature around zero bias for both monolayer and bilayer graphene/SiC, as well as significant spatial inhomogeneity in electronic structure above the gap edge. Nanoscale structure at the SiC/graphene interface is seen to correlate with observed electronic spatial inhomogeneity. These results are important for potential devices involving electronic transport or tunneling in graphene/SiC.

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