Graphene bilayer with a twist: electronic structure

Raman spectroscopy study of rotated double-layer graphene: misorientation-angle dependence of electronic structure

We present a systematic Raman study of unconventionally stacked double-layer graphene, and find that the spectrum strongly depends on the relative rotation angle between layers. Rotation-dependent trends in the position, width and intensity of graphene 2D and G peaks are experimentally established and accounted for theoretically. Our theoretical analysis reveals that changes in electronic band structure due to the interlayer interaction, such as rotational-angle dependent Van Hove singularities, are responsible for the observed spectral features. Our combined experimental and theoretical study provides a deeper understanding of the electronic band structure of rotated double-layer graphene, and leads to a practical way to identify and analyze rotation angles of misoriented double-layer graphene.

Angle-resolved Raman imaging of interlayer rotations and interactions in twisted bilayer graphene

Few-layer graphene is a prototypical layered material, whose properties are determined by the relative orientations and interactions between layers. Exciting electrical and optical phenomena have been observed for the special case of Bernal-stacked few-layer graphene, but structure-property correlations in graphene which deviates from this structure are not well understood. Here, we combine two direct imaging techniques, dark-field transmission electron microscopy (DF-TEM) and widefield Raman imaging, to establish a robust, one-to-one correlation between twist angle and Raman intensity in twisted bilayer graphene (tBLG). The Raman G band intensity is strongly enhanced due to a previously unreported singularity in the joint density of states of tBLG, whose energy is exclusively a function of twist angle and whose optical transition strength is governed by interlayer interactions, enabling direct optical imaging of these parameters. Furthermore, our findings suggest future potential for novel optical and optoelectronic tBLG devices with angle-dependent, tunable characteristics.

Understanding surfactant/graphene interactions using a graphene field effect transistor: relating molecular structure to hysteresis and carrier mobility

Manipulation of transport hysteresis on graphene transistors and understanding electron transfer between graphene and polar/ionic adsorbates are important for the development of graphene-based sensor devices and nonvolatile memory electronics. We have investigated the effects of commonly used surfactants for graphene dispersion in aqueous solution on transport characteristics of graphene transistors. The adsorbates are found to transfer electrons to graphene, scatter carrier transport, and induce additional electron-hole puddles when the graphene is on an SiO(2) substrate. We relate the change in transport characteristics to specific chemical properties of a series of anionic, cationic, and neutral surfactants using a modification of a self-consistent transport theory developed for graphene. To understand the effects of surfactant adsorbates trapped on either side of the graphene, suspended devices were fabricated. Strong hysteresis is observed only when both sides of the graphene were exposed to the surfactants, attributable to their function as charge traps. This work is the first to demonstrate the control of hysteresis, allowing us to eliminate it for sensor and device applications or to enhance it to potentially enable nonvolatile memory applications.

Non-Abelian gauge potentials in graphene bilayers

We study the effect of spatial modulations in the interlayer hopping of graphene bilayers, such as those that arise upon shearing or twisting. We show that their single-particle physics, characterized by charge accumulation and recurrent formation of zero-energy bands as the pattern period L increases, is governed by a non-Abelian gauge potential arising in the low-energy electronic theory due to the coupling between layers. We show that such gauge-type couplings give rise to a potential that, for certain discrete values of L, spatially confines states at zero energy in particular regions of the moiré patterns. We also draw the connection between the recurrence of the flat zero-energy bands and the non-Abelian character of the potential.

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.

Quantum Hall effect, screening, and layer-polarized insulating states in twisted bilayer graphene

We investigate electronic transport in dual-gated twisted-bilayer graphene. Despite the subnanometer proximity between the layers, we identify independent contributions to the magnetoresistance from the graphene Landau level spectrum of each layer. We demonstrate that the filling factor of each layer can be independently controlled via the dual gates, which we use to induce Landau level crossings between the layers. By analyzing the gate dependence of the Landau level crossings, we characterize the finite interlayer screening and extract the capacitance between the atomically spaced layers. At zero filling factor, we observe an insulating state at large displacement fields, which can be explained by the presence of counterpropagating edge states with interlayer coupling.

Quantum Hall effect in twisted bilayer graphene

We address the quantum Hall behavior in twisted bilayer graphene transferred from the C face of SiC. The measured Hall conductivity exhibits the same plateau values as for a commensurate Bernal bilayer. This implies that the eightfold degeneracy of the zero energy mode is topologically protected despite rotational disorder as recently predicted. In addition, an anomaly appears. The densities at which these plateaus occur show a magnetic field dependent offset. It suggests the existence of a pool of localized states at low energy, which do not count towards the degeneracy of the lowest band Landau levels. These states originate from an inhomogeneous spatial variation of the interlayer coupling.

Moire bands in twisted double-layer graphene

A moiré pattern is formed when two copies of a periodic pattern are overlaid with a relative twist. We address the electronic structure of a twisted two-layer graphene system, showing that in its continuum Dirac model the moiré pattern periodicity leads to moiré Bloch bands. The two layers become more strongly coupled and the Dirac velocity crosses zero several times as the twist angle is reduced. For a discrete set of magic angles the velocity vanishes, the lowest moiré band flattens, and the Dirac-point density-of-states and the counterflow conductivity are strongly enhanced.

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.

Bi- and trilayer graphene solutions

Bilayer and trilayer graphene with controlled stacking is emerging as one of the most promising candidates for post-silicon nanoelectronics. However, it is not yet possible to produce large quantities of bilayer or trilayer graphene with controlled stacking, as is required for many applications. Here, we demonstrate a solution-phase technique for the production of large-area, bilayer or trilayer graphene from graphite, with controlled stacking. The ionic compounds iodine chloride (ICl) or iodine bromide (IBr) intercalate the graphite starting material at every second or third layer, creating second- or third-stage controlled graphite intercolation compounds, respectively. The resulting solution dispersions are specifically enriched with bilayer or trilayer graphene, respectively. Because the process requires only mild sonication, it produces graphene flakes with areas as large as 50 µm(2). Moreover, the electronic properties of the flakes are superior to those achieved with other solution-based methods; for example, unannealed samples have resistivities as low as ∼1 kΩ and hole mobilities as high as ∼400 cm(2) V(-1) s(-1). The solution-based process is expected to allow high-throughput production, functionalization, and the transfer of samples to arbitrary substrates.

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.

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.

Curvature-induced D-band Raman scattering in folded graphene

Micro-Raman scattering from folds in single-layer graphene sheets finds a D-band at the fold for both incommensurate and commensurate folding, while the parent single-layer graphene lacks a D-band. A coupled elastic-continuum/tight-binding calculation suggests that this D-band arises from the spatially inhomogeneous curvature around a fold in a graphene sheet. The polarization dependence of the fold-induced D-band further reveals that the inhomogeneous curvature acts as a very smooth, ideal one-dimensional defect along the folding direction.

Stacking-dependent optical conductivity of bilayer graphene

The optical conductivities of graphene layers are strongly dependent on their stacking orders. Our first-principle calculations show that, while the optical conductivities of single-layer graphene (SLG) and bilayer graphene (BLG) with Bernal stacking are almost frequency-independent in the visible region, the optical conductivity of twisted bilayer graphene (TBG) is frequency-dependent, giving rise to additional absorption features due to the band folding effect. Experimentally, we obtain from contrast spectra the optical conductivity profiles of BLG with different stacking geometries. Some TBG samples show additional features in their conductivity spectra, in full agreement with our calculation results, while a few samples give universal conductivity values similar to that of SLG. We propose that those variations of optical conductivity spectra of TBG samples originate from the difference between the commensurate and incommensurate stackings. Our results reveal that the optical conductivity measurements of graphene layers indeed provide an efficient way to select graphene films with desirable electronic and optical properties, which would greatly help the future application of those large-scale misoriented graphene films in photonic devices.

Electronic properties of a biased graphene bilayer

We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system-a biased bilayer. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its four-band and two-band continuum approximations, and the four-band model is shown to always be a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, made out of either SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point for understanding the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, such as the second-nearest-neighbour hopping energies t' (in-plane) and γ(4) (inter-layer), and the on-site energy Δ.

Electronic properties of a biased graphene bilayer

We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system-a biased bilayer. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its four-band and two-band continuum approximations, and the four-band model is shown to always be a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, made out of either SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point for understanding the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, such as the second-nearest-neighbour hopping energies t' (in-plane) and γ(4) (inter-layer), and the on-site energy Δ.

Spectroscopic measurement of interlayer screening in multilayer epitaxial graphene

The substrate-induced charge-density profile in carbon face epitaxial graphene is determined using nondegenerate ultrafast midinfrared pump-probe spectroscopy. Distinct zero crossings in the differential transmission spectra are used to identify the Fermi levels of layers within the multilayer stack. Probing within the transmission window of the SiC substrate, we find the Fermi levels of the first four heavily doped layers to be, respectively, 360, 215, 140, and 93 meV above the Dirac point. The charge screening length is determined to be one graphene layer, in good agreement with theoretical predictions.

Simulation study of aberration-corrected high-resolution transmission electron microscopy imaging of few-layer-graphene stacking

Graphene is a single layer of carbon atoms arranged in a hexagonal lattice. The high carrier mobility and mechanical robustness of single layer graphene make it an attractive material for "beyond CMOS" devices. The current work investigates through high-resolution transmission electron microscopy (HRTEM) image simulation the sensitivity of aberration-corrected HRTEM to the different graphene stacking configurations AAA/ABA/ABC as well as bilayers with rotational misorientations between the individual layers. High-angle annular dark field-scanning transmission electron microscopy simulation is also explored. Images calculated using the multislice approximation show discernable differences between the stacking sequences when simulated with realistic operating parameters in the presence of low random noise.

First direct observation of a nearly ideal graphene band structure

Angle-resolved photoemission and x-ray diffraction experiments show that multilayer epitaxial graphene grown on the SiC(0001) surface is a new form of carbon that is composed of effectively isolated graphene sheets. The unique rotational stacking of these films causes adjacent graphene layers to electronically decouple leading to a set of nearly independent linearly dispersing bands (Dirac cones) at the graphene K point. Each cone corresponds to an individual macroscale graphene sheet in a multilayer stack where AB-stacked sheets can be considered as low density faults.

Tuning the electron-phonon coupling in multilayer graphene with magnetic fields

Magneto-Raman scattering study of the E2g optical phonons in multilayer epitaxial graphene grown on a carbon face of SiC is presented. At 4.2 K in magnetic field up to 33 T, we observe a series of well-pronounced avoided crossings each time the optically active inter-Landau level transition is tuned in resonance with the E2g phonon excitation (at 196 meV). The width of the phonon Raman scattering response also shows pronounced variations and is enhanced in conditions of resonance. The experimental results are well reproduced by a model that gives directly the strength of the electron-phonon interaction.

Scanning tunneling spectroscopy of graphene on graphite

We report low temperature high magnetic field scanning tunneling microscopy and spectroscopy of graphene flakes on graphite that exhibit the structural and electronic properties of graphene decoupled from the substrate. Pronounced peaks in the tunneling spectra develop with increasing field revealing a Landau level sequence that provides a direct way to identify graphene and to determine the degree of its coupling to the substrate. The Fermi velocity and quasiparticle lifetime, obtained from the positions and width of the peaks, provide access to the electron-phonon and electron-electron interactions.

Quenching of the quantum Hall effect in multilayered epitaxial graphene: the role of undoped planes

We propose a mechanism for the quenching of the Shubnikov-de Haas oscillations and the quantum Hall effect observed in epitaxial graphene. Experimental data show that the scattering time of the conduction electron is magnetic field dependent and of the order of the cyclotron orbit period, i.e., it can be much smaller than the zero field scattering time. Our scenario involves the extraordinary graphene n=0 Landau level of the uncharged layers which is pinned at the Fermi level. We find that the coupling between this n=0 Landau level and the conducting states of the doped plane leads to a scattering mechanism having the right magnitude to explain the experimental data.

Quantum interference at the twist boundary in graphene

We explore the consequences of a rotation between graphene layers for the electronic spectrum. We derive the commensuration condition in real space and show that the interlayer electronic coupling is governed by an equivalent commensuration in reciprocal space. The larger the commensuration cell, the weaker the interlayer coupling, with exact decoupling for incommensurate rotations and in the theta-->0 limit. Furthermore, from first-principles calculations we determine that even for the smallest possible commensuration cell the decoupling is effectively perfect, and thus graphene layers will be seen to decouple for all rotation angles.

Epitaxial-graphene/graphene-oxide junction: an essential step towards epitaxial graphene electronics

Graphene-oxide (GO) flakes have been deposited to bridge the gap between two epitaxial-graphene electrodes to produce all-graphene devices. Electrical measurements indicate the presence of Schottky barriers at the graphene/graphene-oxide junctions, as a consequence of the band gap in GO. The barrier height is found to be about 0.7 eV, and is reduced after annealing at 180 degrees C, implying that the gap can be tuned by changing the degree of oxidation. A lower limit of the GO mobility was found to be 850 cm2/V s, rivaling silicon. In situ local oxidation of patterned epitaxial graphene has been achieved.

Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene

We show experimentally that multilayer graphene grown on the carbon terminated SiC(0001[over ]) surface contains rotational stacking faults related to the epitaxial condition at the graphene-SiC interface. Via first-principles calculation, we demonstrate that such faults produce an electronic structure indistinguishable from an isolated single graphene sheet in the vicinity of the Dirac point. This explains prior experimental results that showed single-layer electronic properties, even for epitaxial graphene films tens of layers thick.