We present Kelvin probe force microscopy measurements of single-and few-layer graphene resting on SiO 2 substrates. We compare the layer thickness dependency of the measured surface potential with ab initio density functional theory calculations of the work function for substrate-doped graphene. The ab initio calculations show that the work function of single-and bilayer graphene is mainly given by a variation of the Fermi energy with respect to the Dirac point energy as a function of doping, and that electrostatic interlayer screening only becomes relevant for thicker multilayer graphene. From the Raman G-line shift and the comparison of the Kelvin probe data with the ab initio calculations, we independently find an interlayer screening length in the order of four to five layers. Furthermore, we describe in-plane variations of the work function, which can be attributed to partial screening of charge impurities in the substrate, and result in a nonuniform charge density in single-layer graphene.

The electronic properties of doped bilayer graphene in presence of bottom and top gates have been studied and characterized by means of density-functional theory (DFT) calculations. Varying independently the bottom and top gates it is possible to control separately the total doping charge on the sample and the average external electric field acting on the bilayer. We show that, at fixed doping level, the band-gap at the K point in the Brillouin zone depends linearly on the average electric field, whereas the corresponding proportionality coefficient has a nonmonotonic dependence on doping. We find that the DFT-calculated band-gap at K, for small doping levels, is roughly half of the band-gap obtained with standard tight tinding (TB) approach. We show that this discrepancy arises from an underestimate, in the TB model, of the screening of the system to the external electric field. In particular, on the basis of our DFT results we observe that, when bilayer graphene is in presence of an external electric field, both interlayer and intralayer screenings occur. Only the interlayer screening is included in TB calculations, while both screenings are fundamental for the description of the band-gap opening. We finally provide a general scheme to obtain the full band structure of gated bilayer graphene for an arbitrary value of the external electric field and of doping.

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By computing the double-resonant Raman scattering cross section completely from first principles and including the electron-electron interaction at the GW level, we unravel the dominant contributions for the double-resonant 2D mode in bilayer graphene. We show that, in contrast to previous works, the so-called inner processes are dominant and that the 2D-mode line shape is described by three dominant resonances around the K point. We show that the splitting of the transversal optical (TO) phonon branch in the Γ-K direction, as large as 12  cm(-1) in the GW approximation, is of great importance for a thorough description of the 2D-mode line shape. Finally, we present a method to extract the TO phonon splitting and the splitting of the electronic bands from experimental data.

The Raman shift, broadening, and relative Raman intensities of bilayer graphene are computed as functions of the electron concentration. We include dynamic effects for the phonon frequencies and we consider the gap induced in the band structure of bilayer graphene by an external electric field. We show that from the analysis of the Raman spectra of gated bilayer graphene it is possible to quantitatively identify the amount of charges coming from the atmosphere and from the substrate. These findings suggest that Raman spectroscopy of bilayer graphene can be used to characterize the electrostatic environment of few-layers graphene.

The charge carrier dynamics of photoexcited bismuth generates a Drude response that evolves over time. Our data show that the plasma frequency of bismuth displays an initial increase and a subsequent decay. We have performed ab initio calculations on bulk bismuth within the density functional theory and show that this peculiar behavior is due to local extrema in the valence and conduction bands. It follows that most of the carriers first accumulate in these extrema and reach the Fermi level only 0.6 ps after the photoexcitation.

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In this work we study the behavior of the optical phonon modes in bilayer graphene devices by applying top gate voltage, using Raman scattering. We observe the splitting of the Raman G band as we tune the Fermi level of the sample, which is explained in terms of mixing of the Raman (Eg) and infrared (Eu) phonon modes, due to different doping in the two layers. We theoretically analyze our data in terms of the bilayer graphene phonon self-energy which includes non-homogeneous charge carrier doping between the graphene layers. We show that the comparison between the experiment and theoretical model not only gives information about the total charge concentration in the bilayer graphene device, but also allows to separately quantify the amount of unintentional charge coming from the top and the bottom of the system, and therefore to characterize the interaction of bilayer graphene with its surrounding environment.