We probe the local inhomogeneities in the electronic properties of exfoliated graphene due to the presence of charged impurities in the SiO2 substrate using a combined scanning tunneling and electrostatic force microscope. Contact potential difference measurements using electrostatic force microscopy permit us to obtain the average charge density but it does not provide enough resolution to identify individual charges. We find that the tunneling current decay constant, which is related to the local tunneling barrier height, enables one to probe the electronic properties of graphene distorted at the nanometer scale by individual charged impurities. We observe that such inhomogeneities do not show long range ordering and their surface density obtained by direct counting is consistent with the value obtained by macroscopic charge density measurements. These microscopic perturbations of the carrier density significantly alter the electronic properties of graphene, and their characterization is essential for improving the performance of graphene based devices.
We probe the local inhomogeneities of the electronic properties of graphene at the nanoscale using scanning probe microscopy techniques. First, we focus on the study of the electronic inhomogeneities caused by the graphene-substrate interaction in graphene samples exfoliated on silicon oxide. We find that charged impurities, present in the graphene-substrate interface, perturb the carrier density significantly and alter the electronic properties of graphene. This finding helps to understand the observed device-to-device variation typically observed in graphene-based electronic devices. Second,…
A new mechanism that induces charge density variations in corrugated graphene is proposed. Here it is shown how the interplay between lattice deformations and exchange interactions can induce charge separation, i.e., puddles of electrons and holes, for realistic deformation values of the graphene sheet. The induced charge density lies in the range of $10^{11}-10^{12}$ cm$^{-2}$, which is compatible with recent measurements.
Boltzmann transport theory fails near the linear band-crossing of single-layer graphene and near the quadratic band-crossing of bilayer graphene. We report on a numerical study which assesses the role of inter-band coherence in transport when the Fermi level lies near the band-crossing energy of bilayer graphene. We find that interband coherence enhances conduction, and that it plays an essential role in graphene's minimum conductivity phenomena. This behavior is qualitatively captured by an approximate theory which treats inter-band coherence in a relaxation-time approximation. On the basis o…
We study the changes induced by the effective gauge field due to ripples on the low energy electronic structure of graphene. We show that zero energy Landau levels will form, associated to the smooth deformation of the graphene layer, when the height corrugation, $h$, and the length of the ripple, $l$, are such that $h^2 / (l a) \gtrsim 1$, where $a$ is the lattice constant. The existence of localized levels gives rise to a large compressibility at zero energy, and to the enhancement of instabilities arising from electron-electron interactions including electronic phase separation. The combine…
We report room temperature scanning tunneling microscopy and spectroscopy study of bilayer graphene prepared by mechanical exfoliation on SiO$_2$/Si surface and electrically contacted with gold pads using a mechanical mask. The bulk conductivity shows contribution from regions of varying electron density indicating significant charge inhomogeneity. Large scale topographic images show ripple like structures with a roughness of $\sim$1nm while the small scale atomic resolution images show graphite-like triangular lattice. Local dI/dV-V tunnel spectra have an asymmetric V-shape with the minima lo…
Only one atom thick and not inclined to lattice defects, graphene represents the ultimate crystalline membrane. However, its structure reveals unique features not found in other crystalline membranes, in particular the existence of ripples with wavelength of 100-300 Angstroms. Here, I trace the origin of this difference to the free electrons in the membrane. The deformation energy of the lattice creates a coupling between charge fluctuations and the structure, resulting in ripples on the membrane, correlated with charge inhomogeneities. In graphene this mechanism reproduces the experimental re…
Ultrasound detection is one of the most important nondestructive subsurface characterization tools of materials, whose goal is to laterally resolve the subsurface structure with nanometer or even atomic resolution. In recent years, graphene resonators attracted attention as loudspeaker and ultrasound radio, showing its potential to realize communication systems with air-carried ultrasound. Here we show a graphene resonator that detects ultrasound vibrations propagating through the substrate on which it was fabricated. We achieve ultimately a resolution of $\approx7$~pm/$\mathrm{\sqrt Hz}$ in u…
Using a spatially structured, optical pump pulse with a THz probe pulse, we are able to determine spatial variations of the ultrafast THz photoconductivity with sub-wavelength resolution (75 $μm \approx λ/5$ at 0.8 THz) in a planar graphene sample. We compare our results to Raman spectroscopy and correlate the existence of the spatial inhomogeneities between the two measurements. We find a strong correlation with inhomogeneity in electron density. This demonstrates the importance of eliminating inhomogeneities in doping density during CVD growth and fabrication for photoconductive devices.
We studied the growth of an epitaxial graphene monolayer on Ru(0001). The graphene monolayer covers uniformly the Ru substrate over lateral distances larger than several microns reproducing the structural defects of the Ru substrate. The graphene is rippled with a periodicity dictated by the difference in lattice parameter between C and Ru. The theoretical model predict inhomogeneities in the electronic structure. This is confirmed by measurements in real space by means of scanning tunnelling spectroscopy. We observe electron pockets at the higher parts of the ripples.
We present a systematic study of electron backscattering phenomena during conduction for graphene nanoribbons with single-vacancy scatterers and dimensions within the capabilities of modern lithographic techniques. Our analysis builds upon an \textit{ab initio} parameterized semiempirical model that breaks electron-hole symmetry and nonequilibrium Green's function methods for the calculation of the conductance distribution $g$. The underlying mechanism is based on wavefunction localizations and perturbations that in the case of the first $π-π^*$ plateau can give rise to impurity-like pseudogap…
We study the effect of long-range disorder created by charge impurities on the carrier density distribution of graphene-based heterostructures. We consider heterostructures formed by two graphenic sheets (either single layer graphene, SLG, or bilayer graphene, BLG) separated by a dielectric film. We present results for symmetric heterostructures, SLG-SLG and BLG-BLG, and hybrid ones, BLG-SLG. As for isolated layers, we find that the presence of charged impurities induces strong carrier density inhomogeneities, especially at low dopings where the density landscape breaks up in electron-hole pud…
The problem of electrostatic screening of a charged line by undoped or weakly doped graphene is treated beyond the linear-response theory. The induced electron density is found to be approximately doping independent, n(x)~(log x)^2/x^2, at intermediate distances x from the charged line. At larger x, twin p-n junctions may form if the external perturbation is repulsive for graphene charge carriers. The effect of such inhomogeneities on conductance and quantum capacitance of graphene is calculated. The results are relevant for transport properties of graphene grain boundaries and for local elect…
Graphene on a dielectric substrate exhibits spatial doping inhomogeneities, forming electron-hole puddles. Understanding and controlling the latter is of crucial importance for unraveling many of graphene's fundamental properties at the Dirac point. Here we show the coexistence and correlation of charge puddles and topographic ripples in graphene decoupled from the metallic substrate it was grown on. The analysis of interferences of Dirac fermion-like electrons yields a linear dispersion relation, indicating that graphene on a metal can recover its intrinsic electronic properties.
The charge carrier density in graphene on a dielectric substrate such as SiO$_2$ displays inhomogeneities, the so-called charge puddles. Because of the linear dispersion relation in monolayer graphene, the puddles are predicted to grow near charge neutrality, a markedly distinct property from conventional two-dimensional electron gases. By performing scanning tunneling microscopy/spectroscopy on a mesoscopic graphene device, we directly observe the puddles' growth, both in spatial extent and in amplitude, as the Dirac point is approached. Self-consistent screening theory provides a unified des…
We consider spin effects related to the random spin-orbit interaction in graphene. Such a random interaction can result from the presence of ripples and/or other inhomogeneities at the graphene surface. We show that the random spin-orbit interaction generally reduces the spin dephasing (relaxation) time, even if the interaction vanishes on average. Moreover, the random spin-orbit coupling also allows for spin manipulation with an external electric field. Due to the spin-flip interband as well as intraband optical transitions, the spin density can be effectively generated by periodic electric f…
Doping twisted bilayer graphene away from charge neutrality leads to an enormous buildup of charge inhomogeneities within each Moiré unit cell. Here we show, using unbiased real-space self-consistent Hartree calculations on a relaxed lattice, that Coulomb interactions smoothen this charge imbalance by changing the occupation of earlier identified `ring' orbitals in the AB/BA region and `center' orbitals at the AA region. For hole doping, this implies an increase of the energy of the states at the ${\bf Γ}$ point, leading to a further flattening of the flat bands and a pinning of the Van Hove s…
Coulomb coupling between proximal layers in graphene heterostructures results in efficient energy transfer between the layers. We predict that, in the presence of correlated density inhomogeneities in the layers, vertical energy transfer has a strong impact on lateral charge transport. In particular, for Coulomb drag it dominates over the conventional momentum drag near zero doping. The dependence on doping and temperature, which is different for the two drag mechanisms, can be used to separate these mechanisms in experiment. We predict distinct features such as a peak at zero doping and a mul…
We have used scanning gate microscopy to explore the local conductivity of a current-annealed graphene flake. A map of the local neutrality point (NP) after annealing at low current density exhibits micron-sized inhomogeneities. Broadening of the local e-h transition is also correlated with the inhomogeneity of the NP. Annealing at higher current density reduces the NP inhomogeneity, but we still observe some asymmetry in the e-h conduction. We attribute this to a hole doped domain close to one of the metal contacts combined with underlying striations in the local NP.
We consider a graphene sheet in the vicinity of a substrate, which contains charged impurities. An analytic expression for the probability distribution function of voltage fluctuations due to the charged impurities is derived. The distribution function is shown to be non-Gaussian. The voltage fluctuations lead to the appearance of randomly distributed density inhomogeneities in the graphene plane. We argue that these disorder-induced density fluctuations produce a finite conductivity even at a zero gate voltage in accordance with recent experimental observations. We estimate the width of the m…
Evolution of electronic inhomogeneities with back-gate voltage in graphene on SiO$_2$ was studied using room temperature scanning tunneling microscopy and spectroscopy. The reversal of local contrast in some places in the STS maps and sharp changes in cross-correlations between topographic and conductance maps, when graphene Fermi energy approaches its Dirac point, are attributed to change in charge-state of interface defects. The spatial correlations in the conductance maps, described by two different length scales and their growth during approach to Dirac point, show a qualitative agreement …
Quasi-periodic moiré patterns and their effect on electronic properties of twisted bilayer graphene (TBG) have been intensely studied. At small twist angle $θ$, due to atomic reconstruction, the moiré superlattice morphs into a network of narrow domain walls separating micron-scale AB and BA stacking regions. We use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at these domain walls. The observed features become enhanced in a range of mid-infrared frequencies where the hexagonal boron nitride (hBN), which we use as a TBG substrate, is …
We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The $ν=2$ quantized plateau appears from fields $B \simeq 5$ T and persists up to $B \simeq 80$ T. At high current density, in the breakdown regime, the longitudinal resistance oscillates with a $1/B$ periodicity and an anomalous phase, which we relate to the presence of additional electron reservoirs. The high field experimental data suggest that these reservoirs induce a continuous increase of the carrier density up to the highest available magnetic field, thus en…
We report a combined nano-photocurrent and infrared nanoscopy study of twisted bilayer graphene (TBG) enabling access to the local electronic phenomena at length scales as short as 20 nm. We show that the photocurrent changes sign at carrier densities tracking the local superlattice density of states of TBG. We use this property to identify domains of varying local twist angle by local photo-thermoelectric effect. Consistent with the photocurrent study, infrared nano-imaging experiments reveal optical conductivity features dominated by twist-angle dependent interband transitions. Our results p…
It is widely believed that carrier-density inhomogeneities ("electron-hole puddles") in single-layer graphene on a substrate like quartz are due to charged impurities located close to the graphene sheet. Here we demonstrate by using a Kohn-Sham-Dirac density-functional scheme that corrugations in a real sample are sufficient to determine electron-hole puddles on length scales that are larger than the spatial resolution of state-of-the-art scanning tunneling microscopy.
Anisotropic electronic transport is a possible route towards nanoscale circuitry design, particularly in two-dimensional materials. Proposals to introduce such a feature in patterned graphene have to date relied on large-scale structural inhomogeneities. Here we theoretically explore how a random, yet homogeneous, distribution of zigzag-edged triangular perforations can generate spatial anisotropies in both charge and spin transport. Anisotropic electronic transport is found to persist under considerable disordering of the perforation edges, suggesting its viability under realistic experimenta…
Graphene and its van der Waals (vdW) heterostructures provide a unique and versatile playground for explorations of strongly correlated electronic phases, ranging from unconventional fractional quantum Hall (FQH) states in a monolayer system to a plethora of superconducting and insulating states in twisted bilayers. However, the access to those fascinating phases has been thus far entirely restricted to transport techniques, due to the lack of a robust energy bandgap that makes graphene hard to access optically. Here we demonstrate an all-optical, non-invasive spectroscopic tool for probing el…
We introduce a new method to continuously map inhomogeneities of a moiré lattice and apply it to large-area topographic images we measure on open-device twisted bilayer graphene (TBG). We show that the variation in the twist angle of a TBG device, which is frequently conjectured to be the reason for differences between devices with a supposed similar twist angle, is about 0.08° around the average of 2.02° over areas of several hundred nm, comparable to devices encapsulated between hBN slabs. We distinguish between an effective twist angle and local anisotropy and relate the latter to heterostr…
Pump-probe spectroscopy is central for exploring ultrafast dynamics of fundamental excitations, collective modes and energy transfer processes. Typically carried out using conventional diffraction-limited optics, pump-probe experiments inherently average over local chemical, compositional, and electronic inhomogeneities. Here we circumvent this deficiency and introduce pump-probe infrared spectroscopy with ~20 nm spatial resolution, far below the diffraction limit, which is accomplished using a scattering scanning near-field optical microscope (s-SNOM). This technique allows us to investigate …
Coulomb drag between parallel two-dimensional electronic layers is an excellent tool for the study of electron-electron interactions. In actual experiments, the layers display spatial charge density fluctuations due to imperfections such as external charged impurities. However, at present a systematic way of taking these inhomogeneities into account in drag calculations has been lacking, making the interpretation of experimental data problematic. On the other hand, there exists a highly successful and widely accepted formalism describing transport within single inhomogeneous layers known as ef…
We present a spectroscopic method which utilizes virtual photons to selectively measure the electronic structure of the top-most atomic layer. These virtual photons are created when incident positrons transition from vacuum states to bound surface states on the sample surface and can transfer sufficient energy to excite electrons into the vacuum. The short interaction range of the virtual photons restricts the penetration depth to approximately the Thomas-Fermi screening length. Measurements and analysis of the kinetic energies of the emitted electrons made on a single-layer of graphene deposi…
