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.     

Elastic instability of bilayer graphene using atomistic finite element

In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.     

Graphene bilayer with a twist: electronic structure

We consider a graphene bilayer with a relative small angle rotation between the layers--a stacking defect often seen in the surface of graphite--and calculate the electronic structure near zero energy in a continuum approximation. Contrary to what happens in an AB stacked bilayer and in accord with observations in epitaxial graphene, we find: (a) the low energy dispersion is linear, as in a single layer, but the Fermi velocity can be significantly smaller than the single-layer value; (b) an external electric field, perpendicular to the layers, does not open an electronic gap.     

Features of 30° Moiré Graphene Bilayers with Folded Holes

New nanomeshes with closed holes based on bilayer graphene twisted by 30° are studied. It is found that such structures can have different electronic characteristics (from semiconducting to metallic) depending on the shape of holes. Comparison with the single-layer graphene meshes having holes of similar shapes demonstrates a significant difference of their electronic spectra. The meshes with triangular “folded” holes turn out to be nonmagnetic in contrast to the single-layer meshes with the same holes. The spectra of 30° bilayer graphene nanomeshes exhibit numerous peaks in the electron density of states within a wide energy range. This makes such structures promising for applications in photovoltaics and optoelectronics. Features of 30° Moiré Graphene Bilayers with Folded Holes.     

Minimal conductivity in bilayer graphene

Using the Landauer formula approach, it is proven that minimal conductivity of order e²/h found experimentally in bilayer graphene is an intrinsic property. For the case of ideal crystals, the conductivity turns out to be equal to e²/2h per valley per spin. A zero-temperature shot noise in bilayer graphene is considered and the Fano factor is calculated. Its value 1–2/π is close to the value 1/3 found earlier for single-layer graphene.     

First-principles study of hydrogen adsorption on titanium-decorated single-layer and bilayer graphenes

The adsorption of hydrogen molecules on titanium-decorated （Ti-decorated） single-layer and bilayer graphenes is studied using density functional theory （DFT） with the relativistic effect. Both the local density approximation （LDA） and the generalized gradient approximation （GGA） are used for obtaining the region of the adsorption energy of H2 molecules on Ti-decorated graphene. We find that a graphene layer with titanium （Ti） atoms adsorbed on both sides can store hydrogen up to 9.51 wt% with average adsorption energy in a range from -0.170 eV to 0.518 eV. Based on the adsorption energy criterion, we find that chemisorption is predominant for H2 molecules when the concentration of H2 molecules absorbed is low while physisorption is predominant when the concentration is high. The computation results for the bilayer graphene decorated with Ti atoms show that the lower carbon layer makes no contribution to hydrogen adsorption.     

Time-Dependent Resonant Tunneling in a Double-Barrier Diode Structure

The elastic moduli of bilayer graphene nanomeshes, i.e., nanomeshes of bilayer graphene, where layers at the edges of “closed” holes are coupled to each other by a continuous network of sp²-hybridized atoms, have been calculated by ab initio methods. Structures with different configurations of holes in layers with AA, AB, and 30° stackings have been studied. It has been shown that the ultimate tensile strength of the nanomeshes under consideration is higher than that of graphene nanostructures and is comparable with the ultimate tensile strength of bilayer graphene and single-layer carbon nanotubes. A possible application of such strong nanomeshes as nanocontainers for hydrogen storage and other compressed gases has been also discussed.

     

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.     

Spin relaxation in single-layer and bilayer graphene

We investigate spin relaxation in graphene spin valves and observe strongly contrasting behavior for single-layer graphene (SLG) and bilayer graphene (BLG). In SLG, the spin lifetime (τ(s)) varies linearly with the momentum scattering time (τ(p)) as carrier concentration is varied, indicating the dominance of Elliot-Yafet (EY) spin relaxation at low temperatures. In BLG, τ(s) and τ(p) exhibit an inverse dependence, which indicates the dominance of Dyakonov-Perel spin relaxation at low temperatures. The different behavior is due to enhanced screening and/or reduced surface sensitivity of BLG, which greatly reduces the impurity-induced EY spin relaxation.     

扭转双层石墨烯物理性质、制备方法及其应用的研究进展

石墨烯是一种准二维蜂窝网状结构新型纳米材料,石墨烯的层数和构型对其性能产生重要影响.固体中准粒子的量子状态由其本身的对称性质所决定,扭转双层石墨烯打破了对称性,引起了强烈的层间耦合作用,改变了扭转双层石墨烯的电子能带、声子色散、形成能垒等物性,产生了独特的性能,如可以连续调控带隙0-250 meV,光电效应的响应度相比于单层石墨烯提高了80倍,因此对扭转双层石墨烯功能化研究有重大意义.本文同时还论述了扭转双层石墨烯向类金刚石转变的理论与实验研究进展,发现扭转双层石墨烯呈现出具有类金刚石结构与性能特征.进一步阐述调控扭转双层石墨烯的扭转角度对其内在性能的影响,揭示这种新型纳米结构在原子层次的行为特征.最后介绍了如何调控制备扭转双层石墨,分析其调控机理,讨论了各种制备工艺的不足与发展趋势.因此本文从扭转双层石墨烯的输运性质、晶体结构转变、制备三个方面展开阐述,并对其在先进电子器件领域的潜在应用进行了展望.     

Electronic structures and optical absorption of multilayer graphenes

We study the electronic structures and the optical absorption spectra of the multilayer graphenes in the effective mass approximation. We decompose the Hamiltonian of graphene with an arbitrary thickness into smaller subsystems effectively identical to monolayer or bilayer graphene, and express the optical spectrum as a summation over the subsystems. We include the full band parameters which compose the bulk graphite, and closely study their effects on the band structure. We found that the particular band parameters destroying the electron–hole symmetry can affect the optical spectrum through shift of the absorption edge.     

Mid/far-infrared photo-detectors based on graphene asymmetric quantum wells

We conducted a theoretical study on the electronic properties of a single-layer graphene asymmetric quantum well.Quantification of energy levels is limited by electron–hole conversion at the barrier interfaces and free-electron continuum.Electron–hole conversion at the barrier interfaces can be controlled by introducing an asymmetry between barriers and taking into account the effect of the interactions of the graphene sheet with the substrate.The interaction with the substrate induces an effective mass to carriers,allowing observation of Fabry–P′erot resonances under normal incidence and extinction of Klein tunneling.The asymmetry,between barriers creates a transmission gap between confined states and free-electron continuum,allowing the large graphene asymmetric quantum well to be exploited as a photo-detector operating at mid-and far-infrared frequency regimes.     

Coherent nonlinear electromagnetic response in twisted bilayer and few-layer graphene

The phenomenon of Rabi oscillations far from resonance is described in bilayer and few-layer graphene. These oscillations in the population and polarization at the Dirac point in n-layer graphene are seen in the nth harmonic term in the external driving frequency. The underlying reason behind these oscillations is attributable to the pseudospin degree of freedom possessed by all these systems. Conventional Rabi oscillations, which occur only near resonance, are seen in multiple harmonics in multilayer graphene. However, the experimentally measurable current density exhibits anomalous behaviour only in the first harmonic in all the graphene systems. A fully numerical solution of the optical Bloch equations is in complete agreement with the analytical results, thereby justifying the approximation schemes used in the latter. The same phenomena are also described in twisted bilayer graphene with and without an electric potential difference between the layers. It is found that the anomalous Rabi frequency is strongly dependent on twist angle for weak applied fields – a feature absent in single-layer graphene, whereas the conventional Rabi frequency is relatively independent of the twist angle.     

Excitonic effects of bilayer graphene: A simple approach

The present work investigates the excitonic effects on the bilayer graphene with layers of different thickness under the influence of external electric field through a simple numerical approach. The band structure and energy gap have been calculated using a tight-binding model including parameters like the second-nearest-neighbor-hopping energies t′ (in-plane) and γ (intra-layer) and the on-site energy Δ, in details. The binding energy of exciton for bilayer graphene has been calculated by Wannier model and Hartree–Fock approximation through the Bethe–Salpeter equation. Finally the optical conductivity spectrum of bilayer graphene has been calculated by using the effective mass approximation in two band model.     

Observation of long spin-relaxation times in bilayer graphene at room temperature

We report on the first systematic study of spin transport in bilayer graphene (BLG) as a function of mobility, minimum conductivity, charge density, and temperature. The spin-relaxation time τ(s) scales inversely with the mobility μ of BLG samples both at room temperature (RT) and at low temperature (LT). This indicates the importance of D'yakonov-Perel' spin scattering in BLG. Spin-relaxation times of up to 2 ns at RT are observed in samples with the lowest mobility. These times are an order of magnitude longer than any values previously reported for single-layer graphene (SLG). We discuss the role of intrinsic and extrinsic factors that could lead to the dominance of D'yakonov-Perel' spin scattering in BLG. In comparison to SLG, significant changes in the carrier density dependence of τ(s) are observed as a function of temperature.     

铜表面抗氧化性能与其覆盖石墨烯的层数依赖关系研究

We studied the oxidation resistance of graphene-coated Cu surface and its layer dependence by directly growing monolayer graphene with different multilayer structures coexisted, di-minishing the influence induced by residue and transfer technology. It is found that the Cu surface coated with the monolayer graphene demonstrate tremendous difference in oxidation pattern and oxidation rate, compared to that coated with the bilayer graphene, which is considered to be originated from the strain-induced linear oxidation channel in monolayer graphene and the intersection of easily-oxidized directions in each layer of bilayer graphene, respectively. We reveal that the defects on the graphene basal plane but not the boundaries are the main oxidation channel for Cu surface under graphene protection. Our finding indi-cates that compared to putting forth efforts to improve the quality of monolayer graphene by reducing defects, depositing multilayer graphene directly on metal is a simple and effective way to enhance the oxidation resistance of graphene-coated metals.     

Transport characteristics of a single-layer graphene field-effect transistor grown on 4H-silicon carbide

We have investigated transport characteristics of epitaxial graphene grown on semi-insulating silicon-face 4H-silicon carbide (SiC) substrate by thermal decomposition method in relatively high N₂ pressure atmosphere. We have succeeded in forming 1–2 layers of graphene on SiC in controlled manner. The surface morphology of formed graphene was analyzed by atomic force microscopy (AFM), low-energy electron diffraction (LEED) and low-energy electron microscope (LEEM). We have confirmed single-layer graphene growth in average by this method. Top-gated, single-layer graphene field-effect transistors (FETs) were fabricated on epitaxial graphene grown on 4H-SiC. Increased on/off ratio of nearly 100 at low temperature and extremely small minimum conductance (0.018–0.3 in 4 e²/h) in gated Hall-bar samples suggest possible band-gap opening of single-layer epitaxial graphene grown on Si-face SiC.     

Magnetoexcitons in graphene

Specific features of magnetoexcitons in two-dimensional chiral structures, such as single-layer and bilayer graphene, are analyzed. The theory of magnetoexcitons, which are electron excitations corresponding to the transitions between the Landau levels, is presented for the case of high magnetic field. The effect of the Coulomb interaction, features of the band structure, and applied fields on the energy of magnetoexcitons is studied at different integer filling factors.     

Raman analysis of bilayer graphene film prepared on commercial Cu(0.5 at% Ni) foil

This study reports the Raman analysis of bilayer graphene films prepared on commercial dilute Cu(0.5 at% Ni) foils using atmospheric pressure chemical vapor deposition. A bilayer graphene film obtained on Cu foil is known to have small areas of bilayer (islands) with a significant fraction of non‐Bernal stacking, while that obtained on Cu/Ni is known to grow over a large area with Bernal stacking. In the Raman optical microscope images, a wafer‐scale monolayer and large‐area bilayer graphene films were distinguished and confirmed with Raman spectra intensities ratios of 2D to G peaks. The large‐area part of bilayer graphene film obtained was assisted by Ni surface segregation because Ni has higher methane decomposition rate and carbon solubility compared with Cu. The Raman data suggest a Bernal stacking order in the prepared bilayer graphene film. A four‐point probe sheet resistance of graphene films confirmed a bilayer graphene film sheet resistance distinguished from that of monolayer graphene. A relatively higher Ni surface concentration in Cu(0.5 at% Ni) foil was confirmed with time‐of‐flight secondary ion mass spectrometry. The inhomogeneous distribution of Ni in a foil and the diverse crystallographic surface of a foil (confirmed with proton‐induced X‐ray emission and electron backscatter diffraction, respectively) could be a reason for incomplete wafer‐scale bilayer graphene film. The Ni surface segregation in dilute Cu(0.5 at% Ni) foil has a potential to impact on atmospheric pressure chemical vapor deposition growth of large‐area bilayer graphene film. Copyright © 2015 John Wiley & Sons, Ltd.     

Electronic properties of BN-doped bilayer graphene and graphyne in the presence of electric field

In the present paper, we have used density functional theory to study electronic properties of bilayer graphene and graphyne doped with B and N impurities in the presence of electric field. It has been demonstrated that a band gap is opened in the band structures of the bilayer graphene and graphyne by B and N doping. We have also investigated influence of electric field on the electronic properties of BN-doped bilayer graphene and graphyne. It is found that the band gaps induced by B and N impurities are increased by applying electric field. Our results reveal that doping with B and N, and applying electric field are an effective method to open and control a band gap which is useful to design carbon-based next-generation electronic devices.