Dirac cones and minigaps for graphene on Ir(111)

Carbon nanomaterials for advanced energy conversion and storage

It is estimated that the world will need to double its energy supply by 2050. Nanotechnology has opened up new frontiers in materials science and engineering to meet this challenge by creating new materials, particularly carbon nanomaterials, for efficient energy conversion and storage. Comparing to conventional energy materials, carbon nanomaterials possess unique size-/surface-dependent (e.g., morphological, electrical, optical, and mechanical) properties useful for enhancing the energy-conversion and storage performances. During the past 25 years or so, therefore, considerable efforts have been made to utilize the unique properties of carbon nanomaterials, including fullerenes, carbon nanotubes, and graphene, as energy materials, and tremendous progress has been achieved in developing high-performance energy conversion (e.g., solar cells and fuel cells) and storage (e.g., supercapacitors and batteries) devices. This article reviews progress in the research and development of carbon nanomaterials during the past twenty years or so for advanced energy conversion and storage, along with some discussions on challenges and perspectives in this exciting field.

Lattice mismatch induced nonlinear growth of graphene

As a two-dimensional material, graphene can be obtained via epitaxial growth on a suitable substrate. Recently, an interesting nonlinear behavior of graphene growth has been observed on some metal surfaces, but the underlying mechanism is still elusive. Taking the Ir(111) surface as an example, we perform a mechanistic study on graphene growth using a combined approach of first-principles calculations and kinetic Monte Carlo (kMC) simulations. Small carbon clusters on the terrace or at step sites are studied first. Then, we investigate how these small carbon species are attached to graphene edges. Generally, attachment of carbon atoms is thermodynamically favorable. However, due to substrate effect, there are also some edge sites where graphene growth must proceed via cluster attachment. The overall growth rate is determined by these cluster attachment processes, which have a much lower chance of happening compared to the monomer attachment. On the basis of such an inhomogeneous growth picture, kMC simulations are performed by separating different time scales, and the experimentally found quintic-like behavior is well reproduced. Different nonlinear growth behaviors are predicted for different graphene orientations, which is consistent with previous experiments. Inhomogeneity induced by lattice mismatch revealed in this study is expected to be a universal phenomenon and will play an important role in the growth of many other heteroepitaxial systems.

Phonon dispersion of quasi-freestanding graphene on Pt(111)

High-resolution electron energy loss spectroscopy has been used to probe phonon dispersion in quasi-freestanding graphene epitaxially grown on Pt(111). Loss spectra clearly show different dispersing features related to both acoustic and optical phonons. The present results have been compared with graphene systems which strongly interact with the substrate, i.e. the nearly-flat monolayer graphene (MLG)/Ni(111) and the corrugated MLG/Ru(0001). We found that the phonon dispersion of graphene/Pt(111) reproduces well the behavior of pristine graphite. This could be taken as an indication of the negligible interaction between the graphene sheet and the underlying Pt substrate. The softening of out-of-plane modes observed for interacting graphene/metal interfaces does not occur for the nearly-free-standing graphene/Pt(111).

Ir(111) surface state with giant Rashba splitting persists under graphene in air

We reveal a giant Rashba effect (α(R)≈1.3  eV Å) on a surface state of Ir(111) by angle-resolved photoemission and by density functional theory. It is demonstrated that the existence of the surface state, its spin polarization, and the size of its Rashba-type spin-orbit splitting remain unaffected when Ir is covered with graphene. The graphene protection is, in turn, sufficient for the spin-split surface state to survive in ambient atmosphere. We discuss this result along with indications for a topological protection of the surface state.

Time-resolved two-photon photoemission of unoccupied electronic states of periodically rippled graphene on Ru(0001)

The unoccupied electronic states of epitaxially grown graphene on Ru(0001) have been explored by time- and angle-resolved two-photon photoemission. We identify a Ru derived resonance and a Ru/graphene interface state at 0.91 and 2.58 eV above the Fermi level, as well as three image-potential derived states close to the vacuum level. The most strongly bound, short-lived, and least dispersing image-potential state is suggested to have some quantum-well character with a large amplitude below the graphene hills. The two other image-potential states are attributed to a series of slightly decoupled states. Their lifetimes and dispersions are indicative of electrons moving almost freely above the valley areas of the moiré superstructure of graphene.

Wave-function mapping of graphene quantum dots with soft confinement

Using low-temperature scanning tunneling spectroscopy, we map the local density of states of graphene quantum dots supported on Ir(111). Because of a band gap in the projected Ir band structure around the graphene K point, the electronic properties of the QDs are dominantly graphenelike. Indeed, we compare the results favorably with tight binding calculations on the honeycomb lattice based on parameters derived from density functional theory. We find that the interaction with the substrate near the edge of the island gradually opens a gap in the Dirac cone, which implies soft-wall confinement. Interestingly, this confinement results in highly symmetric wave functions. Further influences of the substrate are given by the known moiré potential and a 10% penetration of an Ir surface resonance into the graphene layer.

Large band gap opening between graphene Dirac cones induced by Na adsorption onto an Ir superlattice

We investigate the effects of Na adsorption on the electronic structure of bare and Ir cluster superlattice-covered epitaxial graphene on Ir(111) using angle-resolved photoemission spectroscopy and scanning tunneling microscopy. At Na saturation coverage, a massive charge migration from sodium atoms to graphene raises the graphene Fermi level by ~1.4 eV relative to its neutrality point. We find that Na is adsorbed on top of the graphene layer, and when coadsorbed onto an Ir cluster superlattice, it results in the opening of a large band gap of Δ(Na/Ir/G) = 740 meV, comparable to the one of Ge and with preserved high group velocity of the charge carriers.

Quantum-confined electronic states in atomically well-defined graphene nanostructures

Despite the enormous interest in the properties of graphene and the potential of graphene nanostructures in electronic applications, the study of quantum-confined states in atomically well-defined graphene nanostructures remains an experimental challenge. Here, we study graphene quantum dots (GQDs) with well-defined edges in the zigzag direction, grown by chemical vapor deposition on an Ir(111) substrate by low-temperature scanning tunneling microscopy and spectroscopy. We measure the atomic structure and local density of states of individual GQDs as a function of their size and shape in the range from a couple of nanometers up to ca. 20 nm. The results can be quantitatively modeled by a relativistic wave equation and atomistic tight-binding calculations. The observed states are analogous to the solutions of the textbook "particle-in-a-box" problem applied to relativistic massless fermions.

Molecular self-assembly at solid surfaces

Self-assembly, the process by which objects initially distributed at random arrange into well-defined patterns exclusively due to their local mutual interactions without external intervention, is generally accepted to be the most promising method for large-scale fabrication of functional nanostructures. In particular, the ordering of molecular building-blocks deposited at solid surfaces is relevant for the performance of many organic electronic and optoelectronic devices, such as organic field-effect transistors (OFETs), organic light-emitting diodes (OLEDs) or photovoltaic solar cells. However, the fundamental knowledge on the nature and strength of the intermolecular and molecule-substrate interactions that govern the ordering of molecular adsorbates is, in many cases, rather scarce. In most cases, the structure and morphology of the organic-metal interface is not known and it is just assumed to be the same as in the bulk, thereby implicitly neglecting the role of the surface on the assembly. However, this approximation is usually not correct, and the evidence gathered over the last decades points towards an active role of the surface in the assembly, leading to self-assembled structures that only in a few occasions can be understood by considering just intermolecular interactions in solid or gas phases. In this work we review several examples from our recent research demonstrating the apparently endless variety of ways in which the surface might affect the assembly of organic adsorbates.

Direct observation of electron confinement in epitaxial graphene nanoislands

One leading question for the application of graphene in nanoelectronics is how electronic properties depend on the size at the nanoscale. Direct observation of the quantized electronic states is central to conveying the relationship between electronic structures and local geometry. Scanning tunneling spectroscopy was used to measure differential conductance dI/dV patterns of nanometer-size graphene islands on an Ir(111) surface. Energy-resolved dI/dV maps clearly show a spatial modulation, indicating a modulated local density of states due to quantum confinement, which is unaffected by the edge configuration. We establish the energy dispersion relation with the quantized electron wave vector obtained from a Fourier analysis of dI/dV maps. The nanoislands preserve the Dirac Fermion properties with a reduced Fermi velocity.

Graphene: Piecing it together

Graphene has a multitude of striking properties that make it an exceedingly attractive material for various applications, many of which will emerge over the next decade. However, one of the most promising applications lie in exploiting its peculiar electronic properties which are governed by its electrons obeying a linear dispersion relation. This leads to the observation of half integer quantum hall effect and the absence of localization. The latter is attractive for graphene-based field effect transistors. However, if graphene is to be the material for future electronics, then significant hurdles need to be surmounted, namely, it needs to be mass produced in an economically viable manner and be of high crystalline quality with no or virtually no defects or grains boundaries. Moreover, it will need to be processable with atomic precision. Hence, the future of graphene as a material for electronic based devices will depend heavily on our ability to piece graphene together as a single crystal and define its edges with atomic precision. In this progress report, the properties of graphene that make it so attractive as a material for electronics is introduced to the reader. The focus then centers on current synthesis strategies for graphene and their weaknesses in terms of electronics applications are highlighted.

Magnetothermoelectric transport in modulated and unmodulated graphene

We draw motivation from recent experimental studies and present a comprehensive study of magnetothermoelectric transport in a graphene monolayer within the linear response regime. We employ the modified Kubo formalism developed for thermal transport in a magnetic field. Thermopower as well as thermal conductivity as a function of the gate voltage of a graphene monolayer in the presence of a magnetic field perpendicular to the graphene plane is determined for low magnetic fields (∼1 T) as well as high fields (∼8 T). We include the effects of screened charged impurities on thermal transport. We find good qualitative and quantitative agreement with recent experimental work on the subject. In addition, in order to analyze the effects of modulation, which can be induced by various means, on the thermal transport in graphene, we evaluate the thermal transport coefficients for a graphene monolayer subjected to a periodic electric modulation in a magnetic field. The results are presented as a function of the magnetic field and the gate voltage.

Band structures of bilayer graphene superlattices

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero-energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of "topological" edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.

Graphene on Ir(111): physisorption with chemical modulation

The nonlocal van der Waals density functional approach is applied to calculate the binding of graphene to Ir(111). The precise agreement of the calculated mean height h = 3.41  Å of the C atoms with their mean height h = (3.38±0.04)  Å as measured by the x-ray standing wave technique provides a benchmark for the applicability of the nonlocal functional. We find bonding of graphene to Ir(111) to be due to the van der Waals interaction with an antibonding average contribution from chemical interaction. Despite its globally repulsive character, in certain areas of the large graphene moiré unit cell charge accumulation between Ir substrate and graphene C atoms is observed, signaling a weak covalent bond formation.

New Dirac fermions in periodically modulated bilayer graphene

We investigate the effect of periodic potentials on the electronic structure of bilayer graphene and show that there is a critical value of the external potential below which new Dirac fermions are generated in the low-energy band structure, and above which a band gap is opened in the system. Our results, obtained from a self-consistent tight-binding calculation, can be simply explained by a two-band continuum model as a consequence of the pseudospin physics in graphene. The findings are robust against changes in the form of the potential, as well as bias voltages between the layers.

Multiple plasmon excitations in adsorbed two-dimensional systems

Using monolayer graphene as a model system for a purely two-dimensional (2D) electron gas, we show by energy electron loss spectroscopy, highly resolved both in energy and momentum, that there is a significant probability for the excitation of not only one but two dispersing losses. The appearance of both losses is independent of the substrate (we tested graphene on the Si face of 6H-SiC(0001), and on Ir(111) without and with an intercalated Na layer), and the ratio of the slope in the dispersion curves varies between 1.4 (SiC) and 2. While the lower dispersion curve can be attributed to the excitation of the sheet plasmon, in agreement with theoretical model calculations, the upper dispersion branch has not been identified before for plasmonic excitations in a 2D electron gas, and we assign it tentatively to the excitation of a multipole sheet plasmon.

Nanophysics in graphene: neutrino physics in quantum rings and superlattices

Electrons in graphene at low energy obey a two-dimensional Dirac equation, closely analogous to that of neutrinos. As a result, quantum mechanical effects when the system is confined or subjected to potentials at the nanoscale may be quite different from what happens in conventional electronic systems. In this article, we review recent progress on two systems where this is indeed the case: quantum rings and graphene electrons in a superlattice potential. In the former case, we demonstrate that the spectrum reveals signatures of 'effective time-reversal symmetry breaking', in which the spectra are most naturally interpreted in terms of effective magnetic flux contained in the ring, even when no real flux is present. A one-dimensional superlattice potential is shown to induce strong band-structure changes, allowing the number of Dirac points at zero energy to be manipulated by the strength and/or period of the potential. The emergence of new Dirac points is shown to be accompanied by strong signatures in the conduction properties of the system.

Highly anisotropic Dirac cones in epitaxial graphene modulated by an island superlattice

We present a new method to engineer the charge carrier mobility and its directional asymmetry in epitaxial graphene by using metal cluster superlattices self-assembled onto the moiré pattern formed by graphene on Ir(111). Angle-resolved photoemission spectroscopy reveals threefold symmetry in the band structure associated with strong renormalization of the electron group velocity close to the Dirac point giving rise to highly anisotropic Dirac cones. We further find that the cluster superlattice also affects the spectral-weight distribution of the carbon bands as well as the electronic gaps between graphene states.

Graphene on Ru(0001): contact formation and chemical reactivity on the atomic scale

Graphene on Ru(0001) is contacted with Au tips of a cryogenic scanning tunneling microscope. The formation and conductance of single-atom contacts vary within the moiré unit cell. Density functional calculations reveal that elastic distortions of the graphene lattice occur at contact due to a selectively enhanced chemical reactivity of C atoms at hollow sites of Ru(0001). Concomitant quantum transport calculations indicate that the graphene-Ru distance determines the conductance variations.

Coupling epitaxy, chemical bonding, and work function at the local scale in transition metal-supported graphene

Resonance tunneling spectroscopy and density functional theory calculations are employed to explore local variations in the electronic surface potential of a single graphene layer grown on Rh(111). A work function modulation of 220 meV is experimentally measured, indicating that the chemical bonding strength varies significantly across the supercell of the Moiré pattern formed when graphene is bonded to Rh(111). In combination with high-resolution images, which provide precise knowledge of the local atomic registry at the carbon-metal interface, we identify experimentally, and confirm theoretically, the atomic configuration of maximum chemical bonding to the substrate. Our observations are at odds with reported trends for other transition metal substrates. We explain why this is the case by considering the various factors that contribute to the bonding at the graphene/metal interface.

Photoemission and density functional theory study of Ir(111); energy band gap mapping

We have performed combined angle-resolved photoemission spectroscopy (ARPES) experiments and density functional theory (DFT) calculations of the electronic structure of the Ir(111) surface, with the focus on the existence of energy band gaps. The investigation was motivated by the experimental results suggesting Ir(111) as an ideal support for the growth of weakly bonded graphene. Therefore, our prime interest was electronic structure around the [Formula: see text] symmetry point. In accordance with DFT calculations, ARPES has shown a wide energy band gap with the shape of a parallelogram centred around the [Formula: see text] point. Within the gap three surface states were identified; one just below the Fermi level and two spin-orbit split surface states at the bottom of the gap.

Structure determination of the coincidence phase of graphene on Ru(0001)

The structure of the commensurate (23x23) phase of graphene on Ru(0001) has been analyzed by quantitative low-energy electron diffraction (LEED)-I(V) analysis and density-functional theory calculations. The I(V) analysis uses Fourier components as fitting parameters to determine the vertical corrugation and the lateral relaxation of graphene and the top Ru layers. Graphene is shown to be strongly corrugated by 1.5 A with a minimum C-Ru distance of 2.1 A. Additionally, lateral displacements of C atoms and a significant buckling in the underlying Ru layers are observed, indicative for strong local C-Ru interactions.

Bandgap opening in graphene induced by patterned hydrogen adsorption

Graphene, a single layer of graphite, has recently attracted considerable attention owing to its remarkable electronic and structural properties and its possible applications in many emerging areas such as graphene-based electronic devices. The charge carriers in graphene behave like massless Dirac fermions, and graphene shows ballistic charge transport, turning it into an ideal material for circuit fabrication. However, graphene lacks a bandgap around the Fermi level, which is the defining concept for semiconductor materials and essential for controlling the conductivity by electronic means. Theory predicts that a tunable bandgap may be engineered by periodic modulations of the graphene lattice, but experimental evidence for this is so far lacking. Here, we demonstrate the existence of a bandgap opening in graphene, induced by the patterned adsorption of atomic hydrogen onto the Moiré superlattice positions of graphene grown on an Ir(111) substrate.

Unique synthesis of few-layer graphene films on carbon-doped Pt(83)Rh(17) surfaces

We report a unique synthesis of single- and few-layer graphene films on carbon-doped Pt(83)Rh(17) surfaces by surface segregation and precipitation. The ultrathin graphene films were characterized by atomic force microscopy, Auger electron spectroscopy, and micro-Raman spectroscopy measurements, providing evidence of graphene film thickness and structural quality. The G and 2D band intensity images from micro-Raman spectroscopy measurements confirm that the graphene films with different coverage have very limited defects. Additionally, the 2D band peak can be well-fitted by a single Lozentian peak, indicating that graphene films are characteristic of single layer graphene. Graphene film thickness can be determined by analysis of Auger spectra, indicating that graphene films after 850 degrees C annealing mainly consist of monolayer graphene. By precise adjustment of annealing temperature, graphene film thickness and area size can be controlled and uniform large-area single-layer and double-layer graphene can be achieved.

Thermodynamic properties of a weakly modulated graphene monolayer in a magnetic field

Theoretical investigation of thermodynamic properties of an electrically modulated graphene monolayer in the presence of a perpendicular magnetic field B is presented. This work is aimed at determining the modulation-induced effects on the thermodynamic properties of graphene. The results obtained are compared with those of conventional two-dimensional electron gas (2DEG) systems realized in semiconductor heterostructures. The one-dimensional periodic potential, due to electric modulation lifts the degeneracy of the Landau levels and converts them into bands whose width oscillates as a function of B. We find commensurability (Weiss) oscillations for small values of B and de Haas-van Alphen (dHvA)-type oscillations at larger values of B. We find that the modulation-induced effects on the thermodynamic properties are enhanced and less damped with temperature in graphene compared with conventional 2DEG systems. Furthermore, we have derived analytic asymptotic expressions which allow us to determine the critical temperature and critical magnetic field for the damping of magnetic oscillations in the thermodynamic quantities considered here.

Growth of dome-shaped carbon nanoislands on Ir(111): the intermediate between carbidic clusters and quasi-free-standing graphene

By combining high-resolution photoelectron spectroscopy and ab initio calculations, we show that carbon nanoislands formed during the growth of a long-range ordered graphene layer on Ir(111) assume a peculiar domelike shape. The understanding of the unusual growth mechanism of these C clusters, which represent an intermediate phase between the strongly coupled carbidic carbon and a quasi-free-standing graphene layer, can provide information for a rational design of graphenelike systems at the nanoscale.

Landau levels and quantum Hall effect in graphene superlattices

We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac point of graphene. Because of these new zero-energy branches, the Landau levels at charge neutral filling become 4(2N + 1)-fold degenerate (with N = 0, 1, 2, ..., tunable by the potential strength and periodicity) with the corresponding Hall conductivity sigma_{xy} showing a step of size 4(2N + 1)e;{2}/h. These theoretical findings are robust against variations in the details of the external potential and provide measurable signatures of the unusual electronic structure of graphene superlattices.

Electronic structure of few-layer epitaxial graphene on Ru(0001)

The electronic structure of epitaxial monolayer, bilayer, and trilayer graphene on Ru(0001) was determined by selected-area angle-resolved photoelectron spectroscopy (micro-ARPES). Micro-ARPES band maps provide evidence for a strong electronic coupling between monolayer graphene and the adjacent metal, which causes the complete disruption of the graphene pi-bands near the Fermi energy. However, the perturbation by the metal decreases rapidly with the addition of further graphene sheets, and already an epitaxial graphene bilayer on Ru recovers the characteristic Dirac cones of isolated monolayer graphene. A graphene trilayer on Ru behaves like free-standing bilayer graphene. Density-functional theory based calculations show that this decoupling is due to the efficient passivation of metal d-states by the interfacial graphene layer.