Scanning tunneling spectroscopy of graphene on graphite

Industrial graphene metrology

Graphene is an allotrope of carbon whose structure is based on one-atom-thick planar sheets of carbon atoms that are densely packed in a honeycomb crystal lattice. Its unique electrical and optical properties raised worldwide interest towards the design and fabrication of future electronic and optical devices with unmatched performance. At the moment, extensive efforts are underway to evaluate the reliability and performance of a number of such devices. With the recent advances in synthesizing large-area graphene sheets, engineers have begun investigating viable methodologies for conducting graphene metrology and quality control at industrial scales to understand a variety of reliability issues including defects, patternability, electrical, and physical properties. This review summarizes the current state of industrial graphene metrology and provides an overview of graphene metrology techniques. In addition, a recently developed large-area graphene metrology technique based on fluorescence quenching is introduced. For each metrology technique, the industrial metrics it measures are identified--layer thickness, edge structure, defects, Fermi level, and thermal conductivity--and a detailed description is provided as to how the measurements are performed. Additionally, the potential advantages of each technique for industrial use are identified, including throughput, scalability, sensitivity to substrate/environment, and on their demonstrated ability to achieve quantified results. The recently developed fluorescence-quenching metrology technique is shown to meet all the necessary criteria for industrial applications, rendering it the first industry-ready graphene metrology technique.

Optical self-energy in graphene due to correlations

In highly correlated systems one can define an optical self-energy in analogy to its quasiparticle (QP) self-energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self-energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta (k) of the charge carriers, the structure in the optical self-energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for k equal to or near the Fermi momentum k(F). Consequently, plasmaronic structures which are associated with momenta near the Dirac point at k = 0 are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. We introduce a method whereby detailed quantitative information on such excitation spectra can be extracted from optical data. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self-energies around k(F) of the lower Dirac cone associated with the occupied states.

Scanning tunnelling microscopy of suspended graphene

Suspended graphene has been studied by STM for the first time. Atomic resolution on mono- and bi-layer graphene samples has been obtained after ridding the graphene surface of contamination via high-temperature annealing. Static local corrugations (ripples) have been observed on both types of structures.

Shifting atomic patterns: on the origin of the different atomic-scale patterns of graphite as observed using scanning tunnelling microscopy

We present an in-depth study of the myriad atomically resolved patterns observed on graphite using the scanning tunnelling microscope (STM) over the past three decades. Through the use of highly resolved atomic resolution images, we demonstrate how the interactions between the different graphene layers comprising graphite affect the local surface atomic charge density and its resulting symmetry orientation, with particular emphasis on interactions that are thermodynamically unstable. Moreover, the interlayer graphene coupling is controlled experimentally by varying the tip-surface interaction, leading to associated changes in the atomic patterns. The images are corroborated by first-principles calculations, further validating our claim that surface graphene displacement, coming both from lateral and vertical displacement of the top graphene layer, forms the basis of the rich variety of atomic patterns observed in STM experiments on graphite.

Electronic properties of graphene: a perspective from scanning tunneling microscopy and magnetotransport

This review covers recent experimental progress in probing the electronic properties of graphene and how they are influenced by various substrates, by the presence of a magnetic field and by the proximity to a superconductor. The focus is on results obtained using scanning tunneling microscopy, spectroscopy, transport and magnetotransport techniques.

Graphite, graphene on SiC, and graphene nanoribbons: Calculated images with a numerical FM-AFM

BACKGROUND

Characterization at the atomic scale is becoming an achievable task for FM-AFM users equipped, for example, with a qPlus sensor. Nevertheless, calculations are necessary to fully interpret experimental images in some specific cases. In this context, we developed a numerical AFM (n-AFM) able to be used in different modes and under different usage conditions.

RESULTS

Here, we tackled FM-AFM image calculations of three types of graphitic structures, namely a graphite surface, a graphene sheet on a silicon carbide substrate with a Si-terminated surface, and finally, a graphene nanoribbon. We compared static structures, meaning that all the tip and sample atoms are kept frozen in their equilibrium position, with dynamic systems, obtained with a molecular dynamics module allowing all the atoms to move freely during the probe oscillations.

CONCLUSION

We found a very good agreement with experimental graphite and graphene images. The imaging process for the deposited nanoribbon demonstrates the stability of our n-AFM to image a non-perfectly planar substrate exhibiting a geometrical step as well as a material step.

Direct measurement of the Fermi energy in graphene using a double-layer heterostructure

We describe a technique which allows a direct measurement of the relative Fermi energy in an electron system by employing a double-layer heterostructure. We illustrate this method by using a graphene double layer to probe the Fermi energy as a function of carrier density in monolayer graphene, at zero and in high magnetic fields. This technique allows us to determine the Fermi velocity, Landau level spacing, and Landau level broadening. We find that the N=0 Landau level broadening is larger by comparison to the broadening of upper and lower Landau levels.

Equations-of-motion method for triplet excitation operators in graphene

The particle-hole continuum in the Dirac sea of graphene has a unique window underneath, which in principle leaves room for bound state formation in the triplet particle-hole channel (Baskaran and Jafari 2002 Phys. Rev. Lett. 89 016402). In this work, we construct appropriate triplet particle-hole operators and, using a repulsive Hubbard-type effective interaction, we employ equations of motion to derive approximate eigenvalue equations for such triplet operators. While the secular equation for the spin density fluctuations gives rise to an equation which is second order in the strength of the short range interaction, the explicit construction of the triplet operators obtained here shows that, in terms of these operators, the second-order equation can be factorized to two first-order equations, one of which gives rise to a solution below the particle-hole continuum of Dirac electrons in undoped graphene.

Long-wavelength local density of states oscillations near graphene step edges

Using scanning tunneling microscopy and spectroscopy, we have studied the local density of states (LDOS) of graphene over step edges in boron nitride. Long-wavelength oscillations in the LDOS are observed with maxima parallel to the step edge. Their wavelength and amplitude are controlled by the energy of the quasiparticles allowing a direct probe of the graphene dispersion relation. We also observe a faster decay of the LDOS oscillations away from the step edge than in conventional metals. This is due to the chiral nature of the Dirac fermions in graphene.

Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3

We report the experimental observation of Landau quantization of molecular beam epitaxy grown Sb{2}Te{3} thin films by a low-temperature scanning tunneling microscope. Different from all the reported systems, the Landau quantization in a Sb{2}Te{3} topological insulator is not sensitive to the intrinsic substitutional defects in the films. As a result, a nearly perfect linear energy dispersion of surface states as a 2D massless Dirac fermion system is achieved. We demonstrate that four quintuple layers are the thickness limit for a Sb{2}Te{3} thin film being a 3D topological insulator. The mechanism of the Landau-level broadening is discussed in terms of enhanced quasiparticle lifetime.

Magneto-Raman scattering of graphene on graphite: electronic and phonon excitations

Magneto-Raman-scattering experiments from the surface of graphite reveal novel features associated to purely electronic excitations which are observed in addition to phonon-mediated resonances. Graphene-like and graphite domains are identified through experiments with ∼1  μm spatial resolution performed in magnetic fields up to 32 T. Polarization resolved measurements emphasize the characteristic selection rules for electronic transitions in graphene. Graphene on graphite displays the unexpected hybridization between optical phonon and symmetric across the Dirac point inter Landau level transitions. The results open new experimental possibilities--to use light scattering methods in studies of graphene under quantum Hall effect conditions.

Renormalization group aspects of graphene

Graphene is a two-dimensional crystal of carbon atoms with fascinating electronic and morphological properties. The low-energy excitations of the neutral, clean system are described by a massless Dirac Hamiltonian in (2+1) dimensions, which also captures the main electronic and transport properties. A renormalization group analysis sheds light on the success of the free model: owing to the special form of the Fermi surface that reduces to two single points in momentum space, short-range interactions are irrelevant and only gauge interactions such as long-range Coulomb or effective disorder can play a role in the low-energy physics. We review these features and briefly discuss other aspects related to disorder and to the bilayer material along the same lines.

Many-body interactions in quasi-freestanding graphene

The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.

Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride

Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point. However, accessing the physics of the low-density region at the Dirac point has been difficult because of disorder that leaves the graphene with local microscopic electron and hole puddles. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult. Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance. Here we use scanning tunnelling microscopy to show that graphene conforms to hBN, as evidenced by the presence of Moiré patterns. However, contrary to predictions, this conformation does not lead to a sizeable band gap because of the misalignment of the lattices. Moreover, local spectroscopy measurements demonstrate that the electron-hole charge fluctuations are reduced by two orders of magnitude as compared with those on silicon oxide. This leads to charge fluctuations that are as small as in suspended graphene, opening up Dirac point physics to more diverse experiments.

Single-layer behavior and its breakdown in twisted graphene layers

We report high magnetic field scanning tunneling microscopy and Landau level spectroscopy of twisted graphene layers grown by chemical vapor deposition. For twist angles exceeding ~3° the low energy carriers exhibit Landau level spectra characteristic of massless Dirac fermions. Above 20° the layers effectively decouple and the electronic properties are indistinguishable from those in single-layer graphene, while for smaller angles we observe a slowdown of the carrier velocity which is strongly angle dependent. At the smallest angles the spectra are dominated by twist-induced van Hove singularities and the Dirac fermions eventually become localized. An unexpected electron-hole asymmetry is observed which is substantially larger than the asymmetry in either single or untwisted bilayer graphene.

Nanoanalysis of graphene layers using scanning probe techniques

Graphene is an almost ideal two-dimensional system. Unlike other two-dimensional electron gas systems realized in silicon or gallium arsenide, the electron wave functions are very close to the surrounding environment. While this causes problems in trying to passivate the surface without reducing the mobility, it does allow direct electrical access to the two-dimensional surface states using scanning probe techniques. In this review, we look at recent advances in the nanoanalytics of the surface and edges of graphene using scanning probe techniques.

Band structure and gaps of triangular graphene superlattices

The general properties of long wavelength triangular graphene superlattices are studied. It is shown that Dirac points with and without gaps can arise at a number of high-symmetry points of the Brillouin zone. The existence of gaps can lead to insulating behaviour at commensurate fillings. Strain and magnetic superlattices are also discussed.

Observation of magnetophonon resonance of Dirac fermions in graphite

Coherent coupling of Dirac fermion magnetoexcitons with an optical phonon is observed in graphite as marked magnetic-field dependent splittings and anticrossing behavior of the two coupled modes. The sharp magnetophonon resonance occurs in regions of the graphite sample with properties of superior single-layer graphene having enhanced lifetimes of Dirac fermions. The greatly reduced carrier broadening to values below the graphene electron-phonon coupling constant explains the appearance of sharp resonances that reveal a fundamental interaction of Dirac fermions.

Geometry, mechanics, and electronics of singular structures and wrinkles in graphene

As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity, and electronics at the limits of their validity. We describe the transport and electronic structure in the neighborhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene. We use a combination of atomistic mechanical simulations, analytical geometry, and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport, and mobility in suspended samples, and how the geometry-generated pseudomagnetic and pseudoelectric fields might disrupt Landau quantization.

Phonon-induced gaps in graphene and graphite observed by angle-resolved photoemission

Mapping by angle-resolved photoemission spectroscopy of the spectral functions of graphite and graphene layers at low temperatures reveals a heretofore unreported gap of ~ 67 meV at normal emission. This gap persists to room temperature and beyond, and diminishes for increasing emission angles. We show that this gap arises from electronic coupling to out-of-plane vibrational modes at the K(¯) point in the surface Brillouin zone in accordance with conservation laws and selection rules governed by quantum mechanics. Our study suggests a new approach for characterizing phonons and electron-phonon coupling in solids.

Density of states and zero Landau Level probed through capacitance of graphene

We report capacitors in which a finite electronic compressibility of graphene dominates the electrostatics, resulting in pronounced changes in capacitance as a function of magnetic field and carrier concentration. The capacitance measurements have allowed us to accurately map the density of states D, and compare it against theoretical predictions. Landau oscillations in D are robust and zero Landau level (LL) can easily be seen at room temperature in moderate fields. The broadening of LLs is strongly affected by charge inhomogeneity that leads to zero LL being broader than other levels.

Landau quantization of topological surface states in Bi2Se3

We report the direct observation of Landau quantization in Bi2Se3 thin films by using a low-temperature scanning tunneling microscope. In particular, we discovered the zeroth Landau level, which is predicted to give rise to the half-quantized Hall effect for the topological surface states. The existence of the discrete Landau levels (LLs) and the suppression of LLs by surface impurities strongly support the 2D nature of the topological states. These observations may eventually lead to the realization of quantum Hall effect in topological insulators.

Doped graphene as tunable electron-phonon coupling material

We present a new way to tune the electron-phonon coupling (EPC) in graphene by changing the deformation potential with electron/hole doping. We show the EPC for highest optical branch at the high symmetry point K acquires a strong dependency on the doping level due to electron-electron correlation not accounted in mean-field approaches. Such a dependency influences the dispersion (with respect to the laser energy) of the Raman D and 2D lines and the splitting of the 2D peak in multilayer graphene. Finally this doping dependence opens the possibility to construct tunable electronic devices through external control of the EPC.

Interaction-induced shift of the cyclotron resonance of graphene using infrared spectroscopy

We report a study of the cyclotron resonance (CR) transitions to and from the unusual n=0 Landau level (LL) in monolayer graphene. Unexpectedly, we find the CR transition energy exhibits large (up to 10%) and nonmonotonic shifts as a function of the LL filling factor, with the energy being largest at half filling of the n=0 level. The magnitude of these shifts, and their magnetic field dependence, suggests that an interaction-enhanced energy gap opens in the n=0 level at high magnetic fields. Such interaction effects normally have a limited impact on the CR due to Kohn's theorem [W. Kohn, Phys. Rev. 123, 1242 (1961)], which does not apply in graphene as a consequence of the underlying linear band structure.

Theory of scanning tunneling spectroscopy of magnetic adatoms in graphene

We examine theoretically the signatures of magnetic adatoms in graphene probed by scanning tunneling spectroscopy (STS). When the adatom hybridizes equally with the two graphene sublattices, the broadening of the local adatom level is anomalous and can scale with the cube of the energy. In contrast to ordinary metal surfaces, the adatom local moment can be suppressed by the proximity of the probing scanning tip. We propose that the dependence of the tunneling conductance on the distance between the tip and the adatom can provide a clear signature for the presence of local magnetic moments. We also show that tunneling conductance can distinguish whether the adatom is located on top of a carbon atom or in the center of a honeycomb hexagon.

How perfect can graphene be?

We have identified the cyclotron resonance response of the purest graphene ever investigated, which can be found in nature on the surface of bulk graphite, in the form of decoupled layers from the substrate material. Probing such flakes with Landau level spectroscopy in the THz range at very low magnetic fields, we demonstrate a superior electronic quality of these ultralow density layers (n_{0} approximately 3 x 10;{9} cm;{-2}) expressed by the carrier mobility in excess of 10;{7} cm;{2}/(V * s) or scattering time of tau approximately 20 ps. These parameters set new and surprisingly high limits for intrinsic properties of graphene and represent an important challenge for further developments of current graphene technologies.

Charge 2e skyrmions in bilayer graphene

Quantum Hall states that result from interaction induced lifting of the eightfold degeneracy of the zeroth Landau level in bilayer graphene are considered. We show that at even filling factors electric charge is injected into the system in the form of charge 2e Skyrmions. This is a rare example of binding of charges in a system with purely repulsive interactions. We calculate the Skyrmion energy and size as a function of the effective Zeeman interaction and discuss the signatures of the charge 2e Skyrmions in the scanning probe experiments.

Evidence for strain-induced local conductance modulations in single-layer graphene on SiO2

Graphene has emerged as an electronic material that is promising for device applications and for studying two-dimensional electron gases with relativistic dispersion near two Dirac points. Nonetheless, deviations from Dirac-like spectroscopy have been widely reported with varying interpretations. Here we show evidence for strain-induced spatial modulations in the local conductance of single-layer graphene on SiO(2) substrates from scanning tunneling microscopic (STM) studies. We find that strained graphene exhibits parabolic, U-shaped conductance vs bias voltage spectra rather than the V-shaped spectra expected for Dirac fermions, whereas V-shaped spectra are recovered in regions of relaxed graphene. Strain maps derived from the STM studies further reveal direct correlation with the local tunneling conductance. These results are attributed to a strain-induced frequency increase in the out-of-plane phonon mode that mediates the low-energy inelastic charge tunneling into graphene.