W e obtain the quasiparticle band structure of ABA and ABC-stacked graphene trilayers through ab initio density functional theory (DFT) and many-body quasiparticle calculations within the GW approximation. To interpret our results, we fit the DFT and GW π bands to a low energy tightbinding model, which is found to reproduce very well the observed features near the K point. The values of the extracted hopping parameters are reported and compared with available theoretical and experimental data. For both stackings, the self energy corrections lead to a renormalization of the Fermi velocity, an effect also observed in previous calculations on monolayer graphene. They also increase the separation between the higher energy bands, which is proportional to the nearest neighbor interlayer hopping parameter γ1. Both features are brought to closer agreement with experiment through the self energy corrections. Finally, other effects, such as trigonal warping, electron-hole asymmetry and energy gaps are discussed in terms of the associated parameters. PACS numbers:Graphene, a 2D sheet of carbon atoms in a honeycomb lattice, has attracted a lot of attention of the scientific community in the last few years due to its unique electronic properties, which lead to several potential applications in nanoelectronics [1,2]. However, since graphene is a zero-gap semiconductor, much of the current effort is directed in finding ways to open a gap for use in electronic devices. In particular, one way to do that is to consider graphene stacks, where a number of layers are stacked on top of each other with a particular arrangement. Much work has been done on bilayer graphene, where it was found that a tunable gap can be opened through application of an external electrical field or through doping [3][4][5][6]. In light of recent experimental progress, graphene trilayers are also attracting increasing attention, revealing electronic properties that depend on the stacking order of the three layers. The two most important stackings are ABA (Bernal) and ABC (rhombohedral), which are shown in Fig. 1. For ABA stacking, the low energy π bands are predicted to consist of a set of monolayer and bilayer-like bands, with linear and quadratic dispersions, respectively [2,7,8]. Therefore, this trilayer is expected to show mixed properties from these two systems, which were already observed experimentally [9]. In the presence of an external electrical field perpendicular to the layers, these bands hybridize and a tunable overlap between the linear and parabolic bands is introduced [10, 11]. In contrast, for ABC stacking, the low energy bands consist of a pair of bands with cubic dispersion, which are very flat near the Fermi level. The large density of states associated with this behavior indicates that many-body interactions might play a crucial role in this case. In fact, there are already a few works in the literature investigating the possibility of different competing phases in this system, such as ferromagnetic order [12], charge and spin-density w...

The nanoscale friction between an atomic force microscopy tip and graphene is investigated using friction force microscopy (FFM). During the tip movement, friction forces are observed to increase and then saturate in a highly anisotropic manner. As a result, the friction forces in graphene are highly dependent on the scanning direction: under some conditions, the energy dissipated along the armchair direction can be 80% higher than along the zigzag direction. In comparison, for highly-oriented pyrolitic graphite (HOPG), the friction anisotropy between armchair and zigzag directions is only 15%. This giant friction anisotropy in graphene results from anisotropies in the amplitudes of flexural deformations of the graphene sheet driven by the tip movement, not present in HOPG. The effect can be seen as a novel manifestation of the classical phenomenon of Euler buckling at the nanoscale, which provides the non-linear ingredients that amplify friction anisotropy. Simulations based on a novel version of the 2D Tomlinson model (modified to include the effects of flexural deformations), as well as fully atomistic molecular dynamics simulations and first-principles density-functional theory (DFT) calculations, are able to reproduce and explain the experimental observations.

We study the energy gap opening in the electronic spectrum of graphene bilayers caused by asymmetric doping. Both substitutional impurities (boron acceptors and nitrogen donors) and adsorbed potassium donors are considered. The gap evolution with dopant concentration is compared to the situation in which the asymmetry between the layers is induced by an external electric field. The effects of adsorbed potassium are similar to that of an electric field, but substitutional impurities behave quite differently, showing smaller band gaps and a large sensitivity to disorder and sublattice occupation.

We study the electronic structure and magnetic properties of h-BN triangular clusters embedded in graphene supercells. We find that, depending on the sizes of the clusters and the graphene separation region between them, spin polarization can be induced through charge doping or can be observed even in the neutral state. For these cases, half-metallicity is observed for certain charged states, which are otherwise metallic. In these half-metallic states, the spin density is concentrated near the edges of the clusters, in analogy to the more common predictions for half-metals in zigzag graphene nanoribbons and h-BN/graphene intercalated nanoribbons. Since experimental realizations of h-BN domains in graphene have already been reported, these heterostructures can be suitable candidates for nanoelectronics and spintronics applications.

We propose a practical realization of a field-effect transistor for phonons. Our device is based on a single ionic polymeric molecule and it gives modulations as large as -25% in the thermal conductance for feasible temperatures and electric field magnitudes. Such effect can be achieved by reversibly switching the acoustic torsion mode into an optical mode through the coupling of an applied electric field to the dipole moments of the monomers. This device can pave the way to the future development of phononics at the nanoscale or molecular scale