Confocal Raman spectroscopy has emerged as a major, versatile workhorse for the non-invasive characterization of graphene. Although it is successfully used to determine the number of layers, the ...quality of edges, and the effects of strain, doping and disorder, the nature of the experimentally observed broadening of the most prominent Raman 2D line has remained unclear. Here we show that the observed 2D line width contains valuable information on strain variations in graphene on length scales far below the laser spot size, that is, on the nanometre-scale. This finding is highly relevant as it has been shown recently that such nanometre-scaled strain variations limit the carrier mobility in high-quality graphene devices. Consequently, the 2D line width is a good and easily accessible quantity for classifying the crystalline quality, nanometre-scale flatness as well as local electronic properties of graphene, all important for future scientific and industrial applications.
The extraordinary thermal and elastic properties of graphene, mainly originating from its unique acoustic phonon branches near Γ point in Brillouin zone, have attracted great attention in its ...fundamental researches and practical applications. Here, we introduce an optical technique to accurately probe longitudinal acoustic (LA) and transverse acoustic (TA) phonon branches of graphene near Γ point by double resonant Raman scattering of the combination phonon modes in the range of 1650−2150 cm−1 along with the overtone 2D' mode at ∼3200 cm−1. The corresponding sound velocities (νTA=12.9km/s,νLA=19.9km/s) of graphene have been accessed, which are about 10% smaller than those of graphite. Based on νTA and νLA, the two-dimensional (2d) elastic stiffness (tension) coefficients c11 and c66, Young's modulus Y2d and Poisson's ratio σ2d can be estimated. The results demonstrate again that double resonant Raman spectroscopy is a powerful tool to probe the fundamental properties of graphene.
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The understanding of interactions between electrons and phonons in atomically thin heterostructures is crucial for the engineering of novel two-dimensional devices. Electron-phonon (el-ph) ...interactions in layered materials can occur involving electrons in the same layer or in different layers. Here we report on the possibility of distinguishing intralayer and interlayer el-ph interactions in samples of twisted bilayer graphene and of probing the intralayer process in graphene/h-BN by using Raman spectroscopy. In the intralayer process, the el-ph scattering occurs in a single graphene layer and the other layer (graphene or h-BN) imposes a periodic potential that backscatters the excited electron, whereas for the interlayer process the el-ph scattering occurs between states in the Dirac cones of adjacent graphene layers. Our methodology of using Raman spectroscopy to probe different types of el-ph interactions can be extended to study any kind of graphene-based heterostructure.
Abstract
Twisted bilayer graphene is a fascinating system due to the possibility of tuning the electronic and optical properties by controlling the twisting angle
$$\theta$$
θ
between the layers. The ...coupling between the Dirac cones of the two graphene layers gives rise to van Hove singularities (vHs) in the density of electronic states, whose energies vary with
$$\theta$$
θ
. Raman spectroscopy is a fundamental tool to study twisted bilayer graphene (TBG) systems since the Raman response is hugely enhanced when the photons are in resonance with transition between vHs and new peaks appear in the Raman spectra due to phonons within the interior of the Brillouin zone of graphene that are activated by the Moiré superlattice. It was recently shown that these new peaks can be activated by the intralayer and the interlayer electron–phonon processes. In this work we study how each one of these processes enhances the intensities of the peaks coming from the acoustic and optical phonon branches of graphene. Resonance Raman measurements, performed in many different TBG samples with
$$\theta$$
θ
between
$$4^{\circ }$$
4
∘
and
$$16^{\circ }$$
16
∘
and using several different laser excitation energies in the near-infrared (NIR) and visible ranges (1.39–2.71 eV), reveal the distinct enhancement of the different phonons of graphene by the intralayer and interlayer processes. Experimental results are nicely explained by theoretical calculations of the double-resonance Raman intensity in graphene by imposing the momentum conservation rules for the intralayer and the interlayer electron–phonon resonant conditions in TBGs. Our results show that the resonant enhancement of the Raman response in all cases is affected by the quantum interference effect and the symmetry requirements of the double resonance Raman process in graphene.
Modern electronic structure calculations are predominantly implemented within the super cell representation in which unit cells are periodically arranged in space. Even in the case of non-crystalline ...materials, defect-embedded unit cells are commonly used to describe doped structures. However, this type of computation becomes prohibitively demanding when convergence rates are sufficiently slow and may require calculations with very large unit cells. Here we show that a hitherto unexplored feature displayed by several 2D materials may be used to achieve convergence in formation- and adsorption-energy calculations with relatively small unit-cell sizes. The generality of our method is illustrated with Density Functional Theory calculations for different 2D hosts doped with different impurities, all of which providing accuracy levels that would otherwise require enormously large unit cells. This approach provides an efficient route to calculating the physical properties of 2D systems in general but is particularly suitable for Dirac-point materials doped with impurities that break their sublattice symmetry.
The magnetic behavior of ultrathin ferromagnetic films deposited on substrates is strongly affected by the properties of the substrate. We investigate the spin pumping rate, interlayer exchange ...coupling, and dynamic exchange coupling between ultrathin ferromagnetic films through palladium, a nonmagnetic substrate that displays strong Stoner enhancement. We find that the interlayer exchange coupling, both in the static and dynamic versions, is qualitatively affected by the electron-electron interaction within the substrate. For instance, the oscillatory behavior that is a hallmark property of the RKKY exchange coupling is strongly suppressed by the induced moment in Pd. Although the spin pumping rate of ferromagnetic films atop palladium is only mildly changed by the electron-electron interaction in Pd, the change is large enough to be detected experimentally. The qualitative aspects of our results for palladium are expected to remain valid for any nonmagnetic substrate where Coulomb repulsion is large.
We study the electronic and optical properties of twisted trilayer and tetralayer graphene structures using a combination of tight-binding and density-functional theory methods. Band structures, ...densities of states, and optical absorption spectra are calculated for a variety of layer stackings and twisting angles. Systematic trends of all properties are obtained and compared to the more well known case of twisted bilayer graphene. For trilayer and tetralayer structures, we find, respectively, two and three well-defined absorption peaks in the infrared/visible range that shift with twisting angle, in contrast to the single peak observed in bilayer graphene. In addition, systems containing Bernal-stacked layers present an extra peak in the infrared which is related to transitions between parabolic bands and does not shift with twisting angle. The observed trends may be used to identify the twisting angle and the number of layers in multilayer graphene samples. In particular, magic angles are predicted for the trilayer and tetralayer structures.
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