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.     

Effect of charged impurity correlations on transport in monolayer and bilayer graphene

We study both monolayer and bilayer graphene transport properties taking into account the presence of correlations in the spatial distribution of charged impurities. In particular we find that the experimentally observed sublinear scaling of the graphene conductivity can be naturally explained as arising from impurity correlation effects in the Coulomb disorder, with no need to assume the presence of short-range scattering centers in addition to charged impurities. We find that also in bilayer graphene, correlations among impurities induce a crossover of the scaling of the conductivity at higher carrier densities. We show that in the presence of correlation among charged impurities the conductivity depends nonlinearly on the impurity density n_i and can increase with n_i.     

NMR of localized magnetic states in graphene

The NMR relaxation rate is studied on the magnetic states of an impurity in bilayer graphene within a tight-binding scenario. The dependencies of the relaxation rate on temperature, interlayer interaction and also the chemical potential have been considered. Although for low temperatures we observe the usual Korringa relation, a characteristic of the conventional fermions, the rate increases with the increase in temperature and tends to saturate for high temperatures. For small interlayer interactions (t_⊥) the system can be either magnetic or non-magnetic. However for higher t_⊥ we observe the existence of only a pure magnetic state. In graphene this transition is also observed with two cusps related to the magnetic to non-magnetic transition, which modifies to a single hump for higher t_⊥, where the system is purely magnetic for any value of chemical potential.     

Electrical and magnetic properties of single crystal [NEt4]2[CuII(mnt)2]

We report electrical and magnetic studies of [NEt₄]₂[Cu^II(mnt)₂]. This crystal is composed of chains of theplanar [Cu^II(mnt)₂]^?2 anions (space group $\text{P}\text{1}$ and z = 1) which exhibit only weak magnetic interactions. The material behaves as a semiconductor; from 300–400°K the conductivity increases by six orders of magnitude and the resistivity values above 300°K are comparable to those of some of the better known wide band-gap inorganic semiconductors. In contrast with the behavior of other linear chain systems, at room temperature the conductivity along the chain (σ_∥) is less than that perpendicular to the chain (σ_⊥). As the temperature is increase, the anisotropy ratio, σ_∥/σ_⊥, becomes greater than unity and increases to 1.6 × 10² at 400°K.     

Phase diagram of the Kohn-Luttinger superconducting state for bilayer graphene

The effect of Coulomb interaction between Dirac fermions on the formation of the Kohn-Luttinger superconducting state in bilayer doped graphene is studied disregarding of the effect of the van der Waals potential of the substrate and impurities. The phase diagram determining the boundaries of superconductive domains with different types of symmetry of the order parameter is built using the extended Hubbard model in the Born weak-coupling approximation with allowance for the intratomic, interatomic, and interlayer Coulomb interactions between electrons. It is shown that the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction inclusively and an account for the long-range intraplane Coulomb interactions significantly affect the competition between the superconducting phases with the f-, p + ip-, and d + id-wave symmetries of the order parameter. It is demonstrated that the account for the interlayer Coulomb interaction enhances the critical temperature of the transition to the superconducting phase.     

Electrical conductivity of nonstoichiometric Ba β-alumina single crystals prepared by a floating zone method

Nonstoichiometric Ba β-alumina single crystals, Ba_1−0.25xMg_1−xAl_10+xO_17+0.25x (0≦x≦1), were prepared in the BaO–MgO–Al₂O₃ system by a floating zone method. The single crystals were cleaved parallel to a (001) plane. The electrical conductivity parallel to the cleavage plane (σ_//) was 10 to 20 times greater than that perpendicular to the cleavage plane (σ_⊥). The σ_// and σ_⊥ had the maximum at around x=0.5. The activation energy of σ_⊥, 240 to 270 kJ/mol, was slightly greater than that of σ_//, 170 to 190 kJ/mol. The σ_// was almost independent of oxygen partial pressure (P_O2), while σ_⊥ showed a P_O2^−1/6 dependence in a low P_O2 region of P_O2=10⁻⁴ to 10⁻¹³ Pa.     

Effect of structural misalignments on the temperature variation of basal plane electrical conductivity of graphite

The amount and extent of structural misaligments in natural graphite crystals have been determined, and the temperature variation of the basal plane electrical conductivity (σ_⊥) of naturally occurring graphite has also been studied from 300 to 90 K. The conductivity (σ_⊥) has been found to obey a law σ_⊥α($\text{1}\text{T}$) down to a certain temperature θ (θ varying from sample to sample), below which the variation deviates from linearity towards lower values of σ_⊥. This behaviour, which was earlier thought to be a characteristic of graphite and whose origin could not be traced, has been shown to be an effect of the structural misalignments usually present in natural samples of graphite.     

Thermal conductivity and magnetic properties of the B substituted Ca3Co4O9

In this study, we reported the effects of the boron (B) substitution into the Ca site in the Ca₃Co₄O₉ system on the electrical, thermal and magnetic properties between 300 K and 5 K. The results indicated that the B-substitution into the system caused an increase of resistivity due to the decrease on carrier concentration. Thermal conductivity decreased for the x = 0.5 B-substituted sample and then increased with increasing the B-content. Analysis on the thermal conductivity of samples showed that the phonon–phonon interaction term is the dominant component in the total thermal conductivity for all the samples. It was found that the point defect contribution to the thermal conductivity increased by increasing the B-content. The temperature dependence of magnetic susceptibility showed a paramagnetic behavior at room temperature and ferrimagnetic behavior below 20 K for unsubstituted sample. But, the magnetization decreased in the B-substituted samples. The substitution of B into the Ca site destroyed the interlayer coupling, which resulted in the decrease of the ferromagnetic behavior. The susceptibility data was fitted using Curie–Weiss law with temperature independent term and the μ_eff values were calculated to be 1.42 μ_B and 3.89 μ_B for unsubstituted sample and the highest B-substitution, respectively.     

Coulomb screening effects on the optoelectronic far-infrared properties of spatially separated few-layer graphene

We investigate the longitudinal optical conductivity of spatially separated few-layer graphene analytically and numerically. Each layer could be monolayer or bilayer graphene. The density–density correlation function has been screened by the dielectric function using the random phase approximation, which includes the inter-layer Coulomb coupling. In the presence of the potential function between the layers, the carrier densities in each layer can be tuned respectively. In these two-dimensional layered structures, the main contributions to the optical conductivity are from the intra- and inter-band transition channels in a same layer. In the infrared region, the Drude optical conductivity was observed by the unscreened intra-band transition process. But in the presence of the inter-layer Coulomb interaction, one peak structure of the optical conductivity is observed which can be modified by the dielectric environment. From the number of turning points and the turning positions, the carrier density, the Fermi wavevector, and the layered structure can be determined.     

Penetration depth and pinning effects in high-Tc superconductors La-Sr-Cu-O and (Er,Ho)-Ba-Cu-O studies by μSR

We report the results of μSR investigations of the ceramic samples La_2-xSr_xCuO_4-σ (x=0.1, 0.15, 0.25) and ReBa₂Cu₃O_7-σ (Re=Er, Ho, Y_0.5Ho_0.5) in the external magnetic field 0–800 Oe. The measurements were performed by the ZFC and FC methods. The irreversibility effects were studied at several temperatures by measuring the mean value and the width of the magnetic field distribution on the muon in the step by step procedure of increasing and subsequent decreasing of the external field. The temperature dependences of the magnetic penetration depth perpendicular to the basal plane λ_⊥ were obtained. For the lanthanum sample with 0.15 of Sr its value at the zero temperature is λ_⊥ (0)=2400 Å, for Er-Ba-Cu-O λ_⊥ (0)=1600 Å.     

The effect of the superconducting–normal proximity on the Josephson tunneling of high-Tc superconductors

The Josephson coupling between two identical high-temperature superconductors was studied theoretically based on a superconducting–normal (SN) bilayer model with s+id-wave pairing in the S layer. It is indicated that due to the proximity effect between S and N layers as the interlayer hopping t_⊥ decreases, the product of the tunneling current through the junction and the normal-state resistance of the junction can be substantially reduced from the value described by the Ambegaokar–Baratoff (AB) theory. Our theoretical result is in good agreement with the experiments.     

Anisotropy of the electrical conductivity in the one-dimensional conductor K2[Pt(CN)4]Br0·30.3(H2O)

Using a method developed by Montgomery we have measured simultaneously σ_| and σ_⊥ the conductivities parallel and perpendicular to the c-axis respectively in single crystals of K₂[Pt(CN)₄]Br_0·30.3(H₂O). The anisotropy $\text{σ}{}_{\mathrm{|}}\text{σ}{}_{\mathrm{\perp }}$ is of the order of 10⁵ at room temperature but decreases to 3.10³ at 35°K.None of the hitherto proposed models allows a detailed comparison between predicted and measured anisotropy. However, the experimental results seem to contradict the two dimensional variable range hopping model. The Bloch, Weisman and Varma model predicts an infinite anisotropy and thus can not be compared with experiment.Recent diffuse X-ray scattering and NMR experiments suggest that the material becomes a band semi-conductor at low temperatures due to a Peierls instability. This model is consistent with our results. While defects and random potentials do not seem to play the dominant rôle assumed in earlier models, they may determine the longitudinal mobility of the excited carriers and hence the anisotropy.     

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.     

Influence of inter cell resonant tunneling on the out-of-plane electronic transport behavior in layered high T<Subscript>c</Subscript> cuprates

The influence of inter unit cell resonant tunneling between the copper-oxygen planes on the c-axis electronic conductivity (σ_c) in normal state of optimal doped bilayer high T_c cuprates like Bi₂Sr₂CaCu₂O_8+x is investigated using extended Hubbard Hamiltonian including resonant tunneling term (T₁₂) between the planes in two adjoining cells. The expression for the out-of-plane (c-axis) conductivity is calculated within Kubo formalism and single particle Green's function by employing Green's function equations of motion technique within meanfield approximation. On the basis of numerical computation, it is pointed out that the renormalized c-axis conductivity increases exponentially with the increment in inter cell resonant tunneling. The effect of T₁₂ on renormalized c-axis conductivity is found to be prominent at low temperatures as compared to temperatures above room temperature (~300 °K). The Coulomb correlation suppresses the variation of renormalized c-axis conductivity with temperature, while renormalized c-axis conductivity increases on increasing carrier concentration. These theoretical results are viewed in terms of existing c-axis transport measurements.     

Self-similar solutions of equations of the nonlinear Schrödinger type

Experimental data are presented for the temperature dependence of the conductivity of Cu: SiO₂ metal-insulator composite films containing 3-nm Cu granules. At low temperatures in the concentration range 17–33 vol % Cu, all of the conductivity curves have a temperature dependence of the form σ ∝ exp{ (T ₀/T)^1/2}, while at higher temperatures a transition is observed to an activational dependence. A numerical simulation of the conduction in a composite material shows that an explanation of the observed temperature dependence must include the Coulomb interaction and the presence of a rather large random potential. The simulation also yields the size dependence and temperature dependence of the mesoscopic scatter of the conductivities of composite conductors. It is shown that a self-selecting percolation channel of current flow is formed in the region of strong mesoscopic scatter.     

Hydrothermal method for the production of reduced graphene oxide

Reduced graphene oxide, RGO (also called chemically modified graphene, CMG) was synthesized by a simple hydrothermal method, with graphite oxide (GO), prepared by the modified Hummers method, served as the raw material. Structural and morphological studies indicate the degree of reduction is dependent on the temperature, which is also verified by Raman analysis. The variation in interlayer distance and the intensity ratio of the D to G Raman modes (I_D/I_G) indicates higher reaction temperature can accelerate the reduction of GO. The conductivity also varies with the degree of reduction, as verified by electrochemical analyzer. Moreover, the reaction process affects organic functional groups, the mechanism during the reaction process is discussed.     

Magnetic susceptibility under pressure and anisotropy of electrical conductivity in quasi-one-dimensional (perylene)2(AsF6)0.75(PF6)0.35 × 0.85CH2Cl2

The magnetic susceptibility and electrical conductivity of the quasi-one-dimensional organic metal (Perylene)₂(AsF₆)_0.75(PF₆)_0.35 × 0.85CH₂Cl₂ was studied in the temperature range 3–300 K. The measured susceptibility can be separated into its defect χ_d, core χ_c and enhanced paramagnetic spin susceptibility χ_p components. χ_p is found to decrease upon lowering the temperature or applying pressure, in analogy with results on charge transfer compounds such as TTF-TCNQ. The conductivity ratio $\text{σ}{}_6\text{σ}{}_{\mathrm{\perp }}$ also decreases with falling temperature. The present results are discussed within the context of a model which takes into account band-narrowing (electron localization) due to strong electron-phonon coupling.     

Magnetic fluctuations in coupled inequivalent Hubbard layers as a model for

We investigate, within the fluctuation-exchange approximation, a correlated-electron model for represented by two inequivalent Hubbard layers coupled by an interlayer hopping . An energy offset is introduced in order to produce a different charge carrier concentration in the two layers. We compare several single-particle and magnetic excitations, namely, the single particle scattering rate, the spectral function and the spin lattice as well as spin-spin relaxation times in the two layers as a function of . We show that the induced interlayer magnetic coupling produces a tendency to “equalization” of the magnetic properties in the two layers whereby antiferromagnetic fluctuations are suppressed in the less doped layer and enhanced in the heavily doped one.The strong antiferromagnetic bilayer coupling causes the charge carriers in the plane with larger doping concentration to behave similar to those of the underdoped layer, they are coupled to. This effect grows for decreasing temperature. For high temperatures or if both layers are optimally or overdoped, i.e. when the antiferromagnetic correlation length becomes of the order or smaller than one lattice site the charge carrier and magnetic dynamics of the two layers is disconnected and the equalization effect disappears. These results are in good agreement with NMR experiments on by Stern et al. [Phys. Rev B 51, 15478 (1995)]. We also compare the results with calculations on bilayer systems with equivalent layers as models for the constituent compounds and . Received: 28 August 1998     

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.     

Plasmon modes of double-layer graphene at finite temperature

We calculate the dynamical dielectric function of doped double-layer graphene (DLG), made of two parallel graphene monolayers with carrier densities n₁ and n₂, and an interlayer separation of d at finite temperature. The results are used to find the dispersion of plasmon modes and loss functions of DLG for several interlayer separations and layer densities. We show that in the case of n₂=0, the finite-temperature plasmon modes are dramatically different from the zero-temperature ones.