Electron spectrum of double-sheet graphene with broken equivalence of sublattices within layers

The electron spectrum of double-sheet graphene composed of sheets with broken equivalence of sublattices, i.e., of gapped (with the gap width 2Δ) graphene sheets, has been calculated. There is a band gap with the width 2Δ in the spectrum of such a system. The influence of the transverse electric field on the electron spectrum of this system has been investigated. It has been shown that the gap width in the presence of the electric field is proportional to the difference |U ? Δ|; i.e., the gap vanishes at U = Δ. This effect can be suggested as an effective method of eliminating an unwanted gap in the spectrum.     

Optical properties of doped graphene layers

The reflectance of a graphene monolayer, as well as of a system of monolayers, is calculated in the infrared range. A quantum expression for the conductivity in the collisionless regime that depends on the frequency, the temperature, and the concentration of carriers is used in the calculations. Above the threshold of the interband electron absorption, the reflectance decreases with increasing frequency. With decreasing temperature, excitation of plasmons in the system of layers is possible in a narrow range near the threshold, which results in the occurrence of a deep and sharp minimum in the frequency dependence of the reflectance.     

Raman spectroscopy of graphene and carbon nanotubes

This paper reviews progress that has been made in the use of Raman spectroscopy to study graphene and carbon nanotubes. These are two nanostructured forms of sp² carbon materials that are of major current interest. These nanostructured materials have attracted particular attention because of their simplicity, small physical size and the exciting new science they have introduced. This review focuses on each of these materials systems individually and comparatively as prototype examples of nanostructured materials. In particular, this paper discusses the power of Raman spectroscopy as a probe and a characterization tool for sp² carbon materials, with particular emphasis given to the field of photophysics. Some coverage is also given to the close relatives of these sp² carbon materials, namely graphite, a three-dimensional (3D) material based on the AB stacking of individual graphene layers, and carbon nanoribbons, which are one-dimensional (1D) planar structures, where the width of the ribbon is on the nanometer length scale. Carbon nanoribbons differ from carbon nanotubes is that nanoribbons have edges, whereas nanotubes have terminations only at their two ends.     

Diamond-like phases prepared from graphene layers

The geometrically optimized structure of ten carbon diamond-like phases obtained by crosslinking graphene layers has been calculated using the density functional theory method and the structural parameters, densities, sublimation energies, and densities of electron states have been determined. Bulk moduli of diamond-like phases have been calculated using the PM3 semiempirical quantum-mechanical method. The X-ray powder diffraction patterns have been calculated based on structural parameters. These diffraction patterns can be used to identify new phases.     

Carrier transport in two-dimensional graphene layers

Carrier transport in gated 2D graphene monolayers is considered in the presence of scattering by random charged impurity centers with density n(i). Excellent quantitative agreement is obtained (for carrier density n>10(12) cm(-2)) with existing experimental data. The conductivity scales linearly with n/n(i) in the theory. We explain the experimentally observed asymmetry between electron and hole conductivities, and the high-density saturation of conductivity for the highest mobility samples. We argue that the experimentally observed saturation of conductivity at low density arises from the charged impurity induced inhomogeneity in the graphene carrier density which becomes severe for n less, similarn(i) approximately 10(12) cm(-2).     

Coulomb drag and magnetotransport in graphene double layers

We review the fabrication and key transport properties of graphene double layers, consisting of two graphene monolayers placed in close proximity, independently contacted, and separated by an ultra-thin dielectric. We outline a simple band structure model relating the layer densities to the applied gate and inter-layer biases, and show that calculations and experimental results are in excellent agreement both at zero and in high magnetic fields. Coulomb drag measurements, which probe the electron–electron scattering between the two layers reveal two distinct regime: (i) diffusive drag at elevated temperatures, and (ii) mesoscopic fluctuation-dominated drag at low temperatures. We discuss the Coulomb drag results within the framework of existing theories.     

Raman spectrum of sodium iodide

Raman spectrum of a single crystal of sodium iodide has been recorded for the first time using λ 2537 excitation. The general features of the spectrum are discussed in the light of the existing theories on the dynamics of the alkali halides.     

Raman spectrum of strontium titanate

The Raman spectrum of strontium titanate has been recorded using λ 4358 of mercury as exciter. The observed spectrum consists of 7 Raman lines, one of which is of low frequency, as expected from the recent theory of Cochran. 6 of these Raman lines have been interpreted as the first order spectrum arising from a small deviation of the cubic strontium titanate from its idealized symmetry. It has been shown that one normal mode of SrTiO₃ neglected by J.T.Last, will be really active in infrared absorption in the region of 440 cm^?1 and that it has to be taken into account in the interpretation of the infrared spectra of titanates. The four vibrational modes of the unit cell of SrTiO₃ correspond to frequencies of 90, 335, 441 and 620 cm^?1 observed in Raman effect. The large width of the Raman lines and the additional lines at 256 cm^?1 and 726 cm^?1 have been attributed to a splitting of the longitudinal and transverse optical modes. With the observed frequencies it has been found possible to account for in a satisfactory manner the specific heat of SrTiO₃ in the range 54·84° K to 1800° K.     

BCS Superconductivity of Dirac electrons in graphene layers

Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and the supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by the existence of a quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point. As distinct from usual superconductors, the supercurrent density is not proportional to the number of electrons but is strongly decreased due to the presence of the Dirac point.     

Raman spectroscopy of magneto-phonon resonances in graphene and graphite

The magneto-phonon resonance or MPR occurs in semiconductor materials when the energy spacing between Landau levels is continuously tuned to cross the energy of an optical phonon mode. MPRs have been largely explored in bulk semiconductors, in two-dimensional systems and in quantum dots. Recently there has been significant interest in the MPR interactions of the Dirac fermion magneto-excitons in graphene, and a rich splitting and anti-crossing phenomena of the even parity $E_{2g}$ long wavelength optical phonon mode have been theoretically proposed and experimentally observed. The MPR has been found to crucially depend on disorder in the graphene layer. This is a feature that creates new venues for the study of interplays between disorder and interactions in the atomic layers. We review here the fundamentals of MRP in graphene and the experimental Raman scattering works that have led to the observation of these phenomena in graphene and graphite.     

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.     

Gauge fields,ripples and wrinkles in graphene layers

We analyze elastic deformations of graphene sheets which lead to effective gauge fields acting on the charge carriers. Corrugations in the substrate induce stresses which, in turn, can give rise to mechanical instabilities and the formation of wrinkles. Similar effects may take place in suspended graphene samples under tension.     

Enhanced Raman scattering of graphene on Ag nanoislands

The effect of Ag nanoislands on the Raman of graphene was investigated in this work. Compared with that on the bare silicon wafer, Raman enhancement was observed in the graphene film that covered on Ag/Si surface with nanoscale Ag islands, which would be induced by the localized plasmon resonance in Ag nanostructures. The interaction between the graphene sheet and Ag/Si substrate was further studied. The peak shift and line shape of Raman spectroscopy indicated a nonuniform strain distribution in the Ag/Si supported graphene film.     

Scanning tunneling microscopy and spectroscopy of graphene layers on graphite

We report low temperature scanning tunneling microscopy and spectroscopy on graphene flakes supported on a graphite substrate. The experiments demonstrate that graphite is exceptionally well suited as a substrate for graphene because it offers support without disturbing the intrinsic properties of the charge carriers. The degree of coupling of a graphene flake to the substrate was recognized and characterized from the appearance of an anomalous Landau level sequence in the presence of a perpendicular magnetic field. By following the evolution of the Landau level spectra along the surface, we identified graphene flakes that are decoupled or very weakly coupled to the substrate. From the Landau level sequence in this flake, we extract the local Fermi velocity and energy of the Dirac point and find extremely weak spatial variation of these quantities confirming the high quality and non invasive nature of the graphite substrate.     

The Raman spectrum of solid cyclopropane

The Raman spectrum of polycrystalline cyclopropane between 3200 and 10 cm^?1 has been recorded. All Raman active fundamentals, two other fundamentals ν₄(A″₁) and ν₇(A″₂), several new crystal components of fundamentals, and many new bands arising from overtones and combinations have been observed.The splittings of the fundamentals, together with the coincidences of infrared and Raman wavenumbers for both fundamentals and lattice modes, are consistent with a C_2v factor group, a C_s site, and two molecules per orthorhombic unit cell.