Localization of π‐electron density in twisted bilayer graphene

In bilayer graphene, mutual rotation of layers has strong effect on the electronic structure. We theoretically study the distribution of electron density in twisted bilayer graphene with the rotation angle of 21.8° and find that regions with AA‐like and AB‐like stacking patterns separately contribute to the interlayer low‐energy van Hove singularities. In order to investigate the peculiarities of interlayer coupling, the charge density map between the layers is examined. The presented results reveal localization of π‐electrons between carbon atoms belonging to different graphene layers when they have AA‐like stacking environment, while the interlayer coupling is stronger within AB‐stacked regions.

Charge density map for bilayer graphene with a layer twist of 21.8° (interlayer region).     

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.     

Strong interlayer coupling in phosphorene/graphene van der Waals heterostructure: A first-principles investigation

Based on first-principles calculations within the framework of density functional theory, we study the electronic properties of phosphorene/graphene heterostructures. Band gaps with different sizes are observed in the heterostructure, and charges transfer from graphene to phosphorene, causing the Fermi level of the heterostructure to shift downward with respect to the Dirac point of graphene. Significantly, strong coupling between two layers is discovered in the band spectrum even though it has a van der Waals heterostructure. A tight-binding Hamiltonian model is used to reveal that the resonance of the Bloch states between the phosphorene and graphene layers in certain K points combines with the symmetry matching between band states, which explains the reason for the strong coupling in such heterostructures. This work may enhance the understanding of interlayer interaction and composition mechanisms in van der Waals heterostructures consisting of two-dimensional layered nanomaterials, and may indicate potential reference information for nanoelectronic and optoelectronic applications.     

Electron-hole pair condensation in a graphene bilayer

The pairing of electrons and holes due to their Coulomb attraction in two parallel, independently gated graphene layers separated by a barrier is considered. At a weak coupling, there exists the BCS-like pair-condensed state. Despite the fact that electrons and holes behave like massless Dirac fermions, the problem of BCS-like electron—hole pairing in the graphene bilayer turns out to be rather similar to that in usual coupled semiconductor quantum wells. The distinctions are due to the Berry phase of electronic wavefunctions and different screening properties. We estimate the values of the gap in a one-particle excitation spectrum for different interlayer distances and carrier concentrations. The influence of the disorder is discussed. At a large enough dielectric susceptibility of the surrounding medium, the weak coupling regime holds at arbitrarily small carrier concentrations. Localized electron—hole pairs are absent in graphene, thus the behavior of the system versus the coupling strength is cardinally different from usual BCS—BEC crossover. The text was submitted by the authors in English.     

Quasi-particle spectrum and density of electronic states in AA- and AB-stacked bilayer graphene

The present work deals with the analysis of the quasi-particle spectrum and the density of states of monolayer and bilayer (AB- and AA-stacked) graphene. The tight binding Hamiltonian containing nearest-neighbor and next-nearest neighbor hopping and onsite Coulomb interaction within two triangular sub-lattice approach for monolayer graphene, along-with the interlayer coupling parameter for bilayer graphene has been employed. The expressions of quasi-particle energies and the density of states (DOS) are obtained within mean-field Green’s function equations of motion approach. It is found that next-nearest-neighbour intralayer hopping introduce asymmetry in the electronic states above and below the zero point energy in monolayer and bilayer (AA- and AB-stacked) graphene. The behavior of electronic states in monolayer and bilayer graphene is different and highly influenced by interlayer coupling and Coulomb interaction. It has been pointed out that the interlayer coupling splits the quasi-particle peak in density of states while the Coulomb interaction suppresses the bilayer splitting and generates a gap at Fermi level in both AA- and AB-stacked bilayer graphene. The theoretically obtained quasi-particle energies and density of states in monolayer and bilayer (AA- and AB-stacked) graphene has been viewed in terms of recent ARPES and STM data on these systems.     

Electronic properties of silicene in BN/silicene van der Waals heterostructures

Silicene is a promising 2D Dirac material as a building block for van der Waals heterostructures(vd WHs). Here we investigate the electronic properties of hexagonal boron nitride/silicene(BN/Si) vd WHs using first-principles calculations.We calculate the energy band structures of BN/Si/BN heterostructures with different rotation angles and find that the electronic properties of silicene are retained and protected robustly by the BN layers. In BN/Si/BN/Si/BN heterostructure, we find that the band structure near the Fermi energy is sensitive to the stacking configurations of the silicene layers due to interlayer coupling. The coupling is reduced by increasing the number of BN layers between the silicene layers and becomes negligible in BN/Si/(BN)_3/Si/BN. In(BN)_n/Si superlattices, the band structure undergoes a conversion from Dirac lines to Dirac points by increasing the number of BN layers between the silicene layers. Calculations of silicene sandwiched by other 2D materials reveal that silicene sandwiched by low-carbon-doped boron nitride or HfO_2 is semiconducting.     

Signatures of strong interlayer coupling in γ-InSe revealed by local differential conductivity

Interlayer coupling in layered semiconductors can significantly affect their optoelectronic properties. However, understanding the mechanisms behind the interlayer coupling at the atomic level is not straightforward. Here, we study modulations of the electronic structure induced by the interlayer coupling in the γ-phase of indium selenide (γ-InSe) using scanning probe techniques. We observe a strong dependence of the energy gap on the sample thickness and a small effective mass along the stacking direction, which are attributed to strong interlayer coupling. In addition, the moiré patterns observed in γ-InSe display a small band-gap variation and nearly constant local differential conductivity along the patterns. This suggests that modulation of the electronic structure induced by the moiré potential is smeared out, indicating the presence of a significant interlayer coupling. Our theoretical calculations confirm that the interlayer coupling in γ-InSe is not only of the van der Waals origin, but also exhibits some degree of hybridization between the layers. Strong interlayer coupling might play an important role in the performance of γ-InSe-based devices.     

Band topology and the quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin-orbit coupling, in order to assess its behavior as a topological insulator. The first Chern number n for the energy bands of single-layer graphene and that for the energy bands of bilayer graphene are computed and compared. It is shown that for a given valley and spin, n for a Bernal-stacked bilayer is doubled with respect to that for the monolayer. This implies that this form of bilayer graphene will have twice as many edge states as single-layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bernal-stacked bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. In contrast, we show that AA-stacked bilayer graphene is not a topological insulator unless the spin-orbit coupling is bigger than the interlayer hopping. Finally, we consider an intermediate situation in which only one of the two layers has spin-orbit coupling, and find that although individual valleys have non-trivial Chern numbers for the case of Bernal stacking, the spectrum as a whole is not gapped, so the system is not a topological insulator.     

A cosmological model for corrugated graphene sheets

Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or other potential defects. In this work we review previous models for topological defects in graphene. A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon–heptagon pairs and Stone-Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.     

Magnetic-state tuning of the rhombohedral graphite film by interlayer spacing and thickness

Based on first-principles total-energy calculations, we systematically investigate how the electronic and magnetic properties of rhombohedral graphite thin films depend on the interlayer spacing and number of layers. Our calculations show that the magnetic ordering of the thin films depends on the interlayer spacing. Thin films under compression normal to the layers possess finite magnetic moments, indicating parallel spin coupling between the two surfaces. We also find that thin graphite films with seven or more atomic layers exhibit magnetic ordering while films with six or less atomic layers are metallic with no magnetic ordering.     

Point defects on graphene on metals

Understanding the coupling of graphene with its local environment is critical to be able to integrate it in tomorrow's electronic devices. Here we show how the presence of a metallic substrate affects the properties of an atomically tailored graphene layer. We have deliberately introduced single carbon vacancies on a graphene monolayer grown on a Pt(111) surface and investigated its impact in the electronic, structural, and magnetic properties of the graphene layer. Our low temperature scanning tunneling microscopy studies, complemented by density functional theory, show the existence of a broad electronic resonance above the Fermi energy associated with the vacancies. Vacancy sites become reactive leading to an increase of the coupling between the graphene layer and the metal substrate at these points; this gives rise to a rapid decay of the localized state and the quenching of the magnetic moment associated with carbon vacancies in freestanding graphene layers.     

Electronic states on the surface of graphite

Graphite consists of graphene layers in an AB (Bernal) stacking arrangement. The introduction of defects can reduce the coupling between the top graphene layers and the bulk crystal producing new electronic states that reflect the degree of coupling. We employ low temperature high magnetic field scanning tunneling microscopy (STM) and spectroscopy (STS) to access these states and study their evolution with the degree of coupling. STS in magnetic field directly probes the dimensionality of electronic states. Thus two-dimensional states produce a discrete series of Landau levels while three-dimensional states form Landau bands providing a clear distinction between completely decoupled top layers and ones that are coupled to the substrate. We show that the completely decoupled layers are characterized by a single sequence of Landau levels with square-root dependence on field and level index indicative of massless Dirac fermions. In contrast weakly coupled bilayers produce special sequences reflecting the degree of coupling, and multilayers produce sequences reflecting the coexistence of massless and massive Dirac fermions. In addition we show that the graphite surface is soft and that an STM tip can be quite invasive when brought too close to the surface and that there is a characteristic tip-sample distance beyond which the effect of sample-tip interaction is negligible.     

Thermal transport in twisted few-layer graphene

Twisted graphene possesses unique electronic properties and applications, which have been studied extensively. Recently, the phonon properties of twisted graphene have received a great deal of attention. To the best of our knowledge,thermal transports in twisted graphene have been investigated little to date. Here, we study perpendicular and parallel transports in twisted few-layer graphene(T-FLG). It is found that perpendicular and parallel transports are both sensitive to the rotation angle θ between layers. When θ increases from 0° to 60°, perpendicular thermal conductivity κ_(||) first decreases and then increases, and the transition angle is θ = 30°. For the parallel transport, the relation between thermal conductivity κand θ is complicated, because intra-layer thermal transport is more sensitive to the edge of layer than their stacking forms. However, the dependence of interlayer scattering on θ is similar to that of κ⊥. In addition, the effect of layer number on the thermal transport is discussed. Our results may provide references for designing the devices of thermal insulation and thermal management based on graphene.     

Theoretical investigation of structural and optical properties of semi-fluorinated bilayer graphene

We have studied the structural and optical properties of semi-fluorinated bilayer graphene using density functional theory. When the interlayer distance is 1.62 , the two graphene layers in AA stacking can form strong chemical bonds.Under an in-plane stress of 6.8 GPa, this semi-fluorinated bilayer graphene becomes the energy minimum. Our calculations indicate that the semi-fluorinated bilayer graphene with the AA stacking sequence and rectangular fluorinated configuration is a nonmagnetic semiconductor(direct gap of 3.46 e V). The electronic behavior at the vicinity of the Fermi level is mainly contributed by the p electrons of carbon atoms forming C=C double bonds. We compare the optical properties of the semifluorinated bilayer graphene with those of bilayer graphene stacked in the AA sequence and find that the semi-fluorinated bilayer graphene is anisotropic for the polarization vector on the basal plane of graphene and a red shift occurs in the [010]polarization, which makes the peak at the low-frequency region located within visible light. This investigation is useful to design polarization-dependence optoelectronic devices.     

Low energy excitations in graphite: The role of dimensionality and lattice defects

In this paper, we present a high resolution angle resolved photoemission spectroscopy (ARPES) study of the electronic properties of graphite. We found that the nature of the low energy excitations in graphite is particularly sensitive to interlayer coupling as well as lattice disorder. As a consequence of the interlayer coupling, we observed for the first time the splitting of the π bands by ≈0.7 eV near the Brillouin zone corner K. At low binding energy, we observed signatures of massless Dirac fermions with linear dispersion (as in the case of graphene), coexisting with quasiparticles characterized by parabolic dispersion and finite effective mass. We also report the first ARPES signatures of electron-phonon interaction in graphite: a kink in the dispersion and a sudden increase in the scattering rate. Moreover, the lattice disorder strongly affects the low energy excitations, giving rise to new localized states near the Fermi level. These results provide new insights on the unusual nature of the electronic and transport properties of graphite.     

Transport properties of AA-stacking bilayer graphene nanoribbons

The transport properties of AA-stacking bilayer graphene nanoribbons (GNs) have been explored by using the nonequilibrium Green's function method and the Landauer–Büttiker formalism. It is found that in the case of zero bias, the interlayer coupling has pronounced effects on the conductance of bilayer GNs. The zigzag bilayer GNs remain metallic, but metallic armchair bilayer GNs will be semiconductor as the strength of interlayer coupling exceeds critical value. The first Van Hove singularities move close to the Dirac point for both armchair and zigzag bilayer GNs with the strength of interlayer coupling increasing. Some prominent conductance peaks around the Fermi energy are observed in zigzag bilayer GNs, when the top layer and bottom layer have different widths. In the presence of bias voltage, the I–V curves show that for armchair bilayer GNs, the interlayer interactions suppress current, while the interlayer interactions have almost no effect on the current for zigzag bilayer GNs. The ripples in bilayer GNs suppress electronic transport, especially for zigzag bilayer GNs.     

Formation of quasi-free graphene on the Ni(111) surface with intercalated Cu,Ag, and Au layers

This paper reports on a study by angle-resolved photoelectron and low-energy electron energy loss spectroscopy of graphene monolayers, which are produced by propylene cracking on the Ni(111) surface, followed by intercalation of Cu, Ag, and Au atoms between the graphene monolayer and the substrate, for various thicknesses of deposited metal layers and annealing temperatures. It has been shown that the spectra of valence-band π states and of phonon vibrational modes measured after intercalation become similar to those characteristic of single-crystal graphite with weak interlayer coupling. Despite the strong coupling of the graphene monolayer to the substrate becoming suppressed by intercalation of Cu and Ag atoms, the π state branch does not reach at the K point of the Brillouin zone the Fermi level, with the graphene coating itself breaking up partially to form graphene domains. At the same time after intercalation of Au atoms, the electronic band structure approaches the closest to that of isolated graphene, with linear π-state dispersion near the K point of the Brillouin zone, and the point of crossing of the filled, (π), with empty, (π*), states lying in the region of the Fermi level, which makes this system a promising experimental model of the quasi-free graphene monolayer.     

Transport properties of AB-stacked bilayer graphene nanoribbons in an electric field

The electronic and thermal properties of AB-stacked bilayer graphene nanoribbons subject to the influences of a transverse electric field are investigated theoretically, including their transport properties. The dispersion relations are found to exhibit a rich dependence on the interlayer interactions, the field strength, and the geometry of the layers. The interlayer coupling will modify the subband curvature, create additional band-edge states, change the subband spacing or energy gap, and separate the partial flat bands. The bandstructures will be symmetric or asymmetric about the Fermi energy for monolayer or bilayer nanoribbons, respectively. The inclusion of a transverse electric field will further alter the bandstructures and lift the degeneracy of the partial flat bands. The chemical-potential-dependent electrical and thermal conductance exhibit a stepwise increase behavior. Variations in the electronic structures with field strength will be reflected in the electrical and thermal conductance. Prominent peaks, as well as single-shoulder and multi-shoulder structures in the electrical and thermal conductance are predicted when varying the electric field strength. The features of the conductance are found to be strongly dependent on the field strength, the geometry, interlayer interactions and temperature.