Session Y12: Graphene: Electronic Structure and Interactions - STM and Nanoribbons

Mapping Dirac Quasiparticles near a Single Coulomb Impurity on Graphene

We have locally mapped the response of charge carriers to a single Coulomb potential placed on a gated graphene device. Scanning tunneling microscopy and spectroscopy were used to fabricate a tunable charge impurity and to measure how Dirac fermions screen it. By mapping spatial variation in the electronic structure of graphene we have directly probed the strength of screened electronic interactions, obtaining a value of epsilon = 3 for the intrinsic graphene dielectric constant. This small value suggests that microscopic electron-electron interactions contribute significantly to intrinsic graphene properties.   

Graphene Tunneling Heterostructures

We have fabricated tunneling heterostructures comprising graphene on boron nitride (BN) substrates and tunnel barriers constructed of exfoliated BN or MoS$_{2}$. We present measurements of the low-temperature tunneling spectrum as a function of the tunneling energy and the carrier density in the graphene, with the latter controlled by a back-gate voltage. We observe a series of tunneling resonances, reminiscent of those seen in STM and planar tunneling experiments on graphene, whose energies disperse with the back-gate voltage.   

Scanning Tunneling Spectroscopy of Graphene on Hexagonal Boron Nitride

Recent work has found hexagonal boron nitride (hBN) to be a good substrate for graphene devices due to its ability to screen charged impurities in the underlying substrate and increase graphene mobility. We investigated graphene on hBN heterostructures using scanning tunneling microscopy and spectroscopy. Because hBN has the same bond structure as graphene with a slightly longer lattice constant, a rotationally dependent Moir\'{e} pattern is formed in graphene on hBN heterostructures. The Moir\'{e} pattern creates a weak periodic potential for the charge carriers in graphene. We performed an experimental and theoretical investigation of its effect on the local density of states. We observed a Moir\'{e} wavelength dependent modification of the local density of states in good agreement with theory predictions.   

Local spontaneous time-reversal symmetry breaking and interacting Dirac fermions in strained CVD-grown graphene on copper

Atomically resolved imaging and spectroscopy of CVD-grown graphene on Cu are studied using scanning tunneling microscopy and spectroscopy. Under strain-induced giant pseudo-magnetic fields (\textit{B$_{S}$}), quantized Landau levels are manifested by peaks of density of states (DOS) at quantized energies. While global time-reversal symmetry is preserved, local spontaneous time-reversal symmetry breaking (TRSB) for the two inequivalent lattice sites due to opposite \textit{B$_{S}$} directions is evidenced by the presence or absence of the zero-mode tunneling conductance peak, confirming theoretical predictions for gauge fields in graphene causing local TRSB while preserving the chiral symmetry. Additionally, the finding of both integer and fractional quantum Hall states due to strain-induced \textit{B$_{S}$} may be attributed to significant short-range Coulomb interactions of Dirac fermions in graphene mediated by the underlying Cu substrate, which yields an onsite Coulomb interaction \textit{U} $\sim$ 3.2 eV larger than the nearest-neighbor hopping energy \textit{t} $\sim$ 2.8 eV. Finally, effects on the DOS of graphene due to pseudo-magnetic fields are compared with those due to applied fields. This work was supported by NSF.   

Real-Space Magnitude and Spatial Extent of the Surface Charge Density of Graphene

The discovery of graphene, a unique two-dimensional electron system with extraordinary physical properties, has ignited tremendous research activity in both science and technology. One such extraordinary property is its enormous current-carrying capacity of 1$\mu $A per atomic row. Fundamentally, this suggests that graphene possesses an unusually large electronic density of states (DOS). Surprisingly, a detailed atomic-scale investigation of the DOS has yet to be completed. Here we present, for the first time, variable-current scanning tunneling microscopy (STM) images, which reveal an unusual three-dimensional picture of graphene's orbitals. Furthermore, density functional theory was used to simulate the variable-current STM images. From this we found that the orbitals expand to fill the holes in the honeycomb structure, making atomic-resolution STM more difficult at lower currents. Also, we discovered that the wavefunctions expand into the vacuum an unusually large amount. Identical studies were performed on graphite, revealing that the DOS of graphene is 300\% larger. Other significant differences found between graphite and graphene will be discussed.   

Direct Imaging of Intrinsic Molecular Orbitals Using Graphene-based Moir\'e Pattern

Direct imaging of the intrinsic electronic structure at high resolution is of both fundamental and technological importance for investigating molecular interaction and mechanisms. Metallic or semiconducting materials are commonly used as substrates for molecular adsorption. Generally, the strong interactions between molecules and these substrates significantly change the intrinsic electronic and geometric structures of the adsorbed molecules. In order to overcome this problem, much effort has been made by passivating substrates with various buffer layers, for instance, thin organic films, NaCl, and oxides. We demonstrate the graphene grown epitaxially on Ru(0001) can be used as a buffer layer to study the intrinsic electronic properties of adsorbed molecules. The intrinsic molecular orbitals of C60, pentacene and perylene-3,4,9,10-tetracarboxylic dianhydride molecules were imaged by scanning tunneling microscope (STM). High resolution STM images of the molecules reveal that the graphene layer decouples the individual molecules electronically from the metallic substrate, which is also verified by density functional theory calculations.   

Tip Induced doping effects in the local tunnel spectra of graphene

We report on tip induced carrier density changes in local tunnel spectra of single layer graphene (SLG) with backgate using room-temperature scanning tunneling microscopy (STM) and spectroscopy. The SLG samples, prepared by exfoliation method and verified by Raman spectra, show atomically resolved honeycomb lattice. Local tunnel spectra show two minima with the two moving in opposite directions along the bias axis. One minimum shows nearly a square-root dependence, and the other shows a linear dependence on the gate voltage. We understand these features as arising from the STM tip induced and bias voltage dependent change in carrier density in SLG. Other than the tip induced doping we also see the effect of charge inhomogeneity on the local tunnel spectra of SLG. The charge inhomogeneity is also seen in bilayer graphene but no new features due to tip induced doping are observed in the local spectra.   

Electronic Structures of Graphene on Ru(0001): Scanning Tunneling Spectroscopy Study

Graphene has inspired remarkable advances in nanotechnology due to its unusual electronic band structures represented by massless Dirac cones. Graphene can be epitaxially grown on metal surfaces by chemical vapor deposition method. Due to the lattice mismatch, epitaxial graphene grown on Ru(0001) shows hexagonal Moir\'e patterns with subatomic height variations. We studied local electronic structures of the epitaxial graphene using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Different spectra were observed at top, bridge, and hollow regions of the Moir\'e patterns. Observed STS data will be explained with structural models.   

Fourier transform-STM: signatures of impurity scattering in graphene ribbons

We report results of a theoretical investigation of the effects of impurity scattering on the Fourier transformed local density of states (FT-LDOS) in graphene ribbons. We derive analytic expressions, within the Dirac approximation, for the Green's functions for armchair ribbons. Utilizing these, we show that the FT-LDOS contains distinct features that can be understood in terms of intra- and intersubband scattering processes. The ribbon band structure can then be reconstructed from the FT-LDOS. This makes the FT-LDOS a valuable spectroscopic tool. These predictions can be directly confirmed by Fourier transform scanning tunneling microscopy.   

Tunable gap graphene micro-ribbons for terahertz plasmonics

Maxwell's equations are solved for an array of graphene micro-ribbons located at the interface between a vacuum half-space and a half-space of a dielectric substrate. Our calculations are include mode-mixing in the optical-response function. A closed-form analytic expression is obtained for the nonlocal optical-response function of a graphene layer with an induced energy gap which is then employed in our calculations beyond the long-wavelength approximation. Both the reflectivity and transmissivity spectral functions are calculated. Specifically, we obtain their dependences on the period of the array, the ribbon width, chemical potential of doped graphene, energy gap between the valence and conduction bands, substrate refractive index, and incident angle of a plane-wave electromagnetic field. Additionally, a qualitative comparison is made between our calculated results in this paper and the recent experimental data given by Ju, {\em et al.\/}, [Nature Nanotechnology, {\bf 6}, 630 (2011)].   

Electron-phonon coupling effects in the (8-5-5) line defect of graphene nanoribbon

A ``metallic'' line defect in graphene nanoribbon consisting of alternating units of octagon and a pair of pentagons (8-5-5) is modeled using the adapted Su-Schrieffer-Heeger model Hamiltonian to include explicit electron-phonon coupling effects. Our results indicate that the 8-5-5 line defect has a finite optical gap of 0.4 eV with a broken charge conjugation symmetry, the bottom conduction band state mimic the nanoribbon edge case and the top valence state identical to the polyacetylene case. Upon photoexcitation, a small self-localized polaron state is found along one zigzag side of the line defect and a soliton-antisoliton pair is found on the other side. When the line defect is sandwiched between two graphene nanoribbons, the finite optical gap and photo-induced self-localized states persist as long as the nanoribbon width is smaller than 2 nm.   

One Dimensional Massless Dirac Fermions in Functionalized Graphene Nanoribbons

Low-energy excitations of graphene are massless Dirac fermions due to presence of linear bands crossing at the Fermi level. Zigzag-edged nanoribbons of graphene (ZGNR), however, being semiconducting, do not possess this property. Using ab initio density-functional theory calculations we find that it is possible to close the band gap of ZGNRs through edge-functionalization with Na atoms. Moreover, the resulting band structure displays tilted-v-shaped linear bands crossing at the Fermi level, corresponding to one-dimensional massless Dirac fermions. We discuss mechanism of formation of such a band structure and its consequences in terms of electronic and transport properties.   

Band Structure Measurements of Bottom-up Fabricated Graphene Nanoribbons

Along with the growing interest in graphene, other low-dimensional carbon nanostructures are currently in the focus of research since these materials offer a wide variety of properties interesting e.g. for nanotechnology application. Among these carbon systems, quasi-one-dimensional graphene nanoribbons (GNR) introduce a possibility to tune the electronic structure - for example, GNRs exhibit a band gap which is inversely proportional to their width and can thus be adjusted over a wide range. While many theoretical studies have been published on the band structure of GNRs, experiments are usually limited by the quality of the GNRs' fabrication, e.g. using lithography or unzipping of carbon nanotubes. In order to avoid defects and irregular edges that are inevitable in these methods, lately a surface-assisted bottom-up synthesis has been demonstrated which yields quasi-perfect GNR structures. [1] In the present study we employ complementary surface-sensitive spectroscopies to investigate occupied and unoccupied bands and the band gap in an armchair GNR which has been synthesized on the Au(111) surface. DFT calculations were performed to obtain a thorough understanding of the nature of the observed states.\\[4pt] [1] J. Cai \emph{et al.}, Nature (London) {\bf466}, 470-473 (2010)   

Synthesis and characterization of nitrogen-doped graphitic nanoribbons

Nitrogen doping of carbon nanostructures such as nanotubes and graphene is a practical approach for tailoring their electronic and chemical properties. However, the doping of graphene nanoribbons still remains to be a challenge. Here we discuss a novel synthetic route to N-doped graphitic nanoribbons using chemical vapor deposition. The morphology of the new nanomaterial resembles the observed for the undoped graphitic nanoribbons, with particular differences specially at the ribbons' edges. We performed scanning and transmission electron microscopy as well as Raman and X-ray photoelectron spectroscopies in order to confirm the nitrogen presence within the nanoribbons. In addition, the electrical response for individual nanoribbons was obtained. We observed that N-doped nanoribbons exhibit a clear semiconductor-like behavior depending on the amount of nitrogen embedded in the hexagonal carbon network (undoped nanoribbons always showed a metallic response). These doped nanostructures could find applications in the fabrication of electronic devices.   

Graphyne- and Graphdiyne-based Nanoribbons: Density Functional Theory Calculations of Electronic Structures

Graphdiyne, a carbon allotrope, which has the same symmetry as graphene and has butadiyne linkages between its nearest-neighbor hexagonal rings, has recently synthesized and fabricated on copper, showing experimentally the semiconductor property with conductivity of 2.516 $\times$ 10$^{-4}$ S m$^{-1}$, which is comparable to silicon. We investigate the configurations and electronic properties of graphyne and graphdiyne nanoribbons with armchair and zigzag edges by using first principles calculations. Our results show that all the nanoribbons are semiconductors with suitable band gaps similar to silicon. And their band gaps decrease as widths of nanoribbons increase. We also find that the band gap is at the $\Gamma$ point for all graphdiyne ribbons and it is at the X point for all graphyne ribbons. Of particular interest, the band gap of zigzag graphyne nanoribbons show a unique ``step effect'' as the width increases. This property is good for tuning of the energy band gap, as in a certain range of the ribbon width, the energy gap remains constant and in reality the edge cannot be as neat as that in a theoretic model. Graphyne and graphdiyne with tunable gaps are promising candidates for future carbon-based electronic devices.