Renormalization of Coulomb interaction in graphene: computing observable quantities

We address the computation of physical observables in graphene in the presence of Coulomb interactions of density-density type modeled with a static Coulomb potential within a quantum field theory perturbative renormalization scheme. We show that all the divergences encountered in the physical quantities are associated to the one loop electron self-energy and can be determined without ambiguities by a proper renormalization of the Fermi velocity. The renormalization of the photon polarization to second order in perturbation theory - a quantity directly related to the optical conductivity - is given as an example.Comment: 8 pages, 4 figure

Anisotropic Fermi surfaces and Kohn-Luttinger superconductivity in two dimensions

The instabilities induced on a two-dimensional system of correlated electrons by the anisotropies of its Fermi line are analyzed on general grounds. Simple scaling arguments allow to predict the opening of a superconducting gap with a well-defined symmetry prescribed by the geometry of the Fermi line. The same arguments predict a critical dimension of 3/2 for the transition of the two-dimensional system to non-Fermi liquid behavior. The methods are applied to the t-t' Hubbard model in a wide range of dopings.Comment: 25 pages, 13 postscript figure

Existence and topological stability of Fermi points in multilayered graphene

We study the existence and topological stability of Fermi points in a graphene layer and stacks with many layers. We show that the discrete symmetries (spacetime inversion) stabilize the Fermi points in monolayer, bilayer and multilayer graphene with orthorhombic stacking. The bands near $k=0$ and $\epsilon=0$ in multilayers with the Bernal stacking depend on the parity of the number of layers, and Fermi points are unstable when the number of layers is odd. The low energy changes in the electronic structure induced by commensurate perturbations which mix the two Dirac points are also investigated.Comment: 6 pages, 6 figures. Expanded version as will appear in PR

Electronic properties of curved graphene sheets

A model is proposed to study the electronic structure of slightly curved graphene sheets with an arbitrary number of pentagon-heptagon pairs and Stone-Wales defects based on a cosmological analogy. The disorder induced by curvature produces characteristic patterns in the local density of states that can be observed in scanning tunnel and transmission electron microscopy.Comment: Corrected versio

Pinning and switching of magnetic moments in bilayer graphene

We examine the magnetic properties of the localized states induced by lattice vacancies in bilayer graphene with an unrestricted Hartree-Fock calculation. We show that with realistic values of the parameters and for experimentally accessible gate voltages we can have a magnetic switching between an unpolarized and a fully polarized system.Comment: 9 pages, 4 figure

Andalucía assesses the investment needed to deploy a fiber-optic network

The setup of fiber-optic telecommunication networks involves high investment efforts. The Regional Government of Andalusia assigned us the development of a tool capable of evaluating the deployment cost of a network that was not to be limited only to connecting large cities, but also to include smaller towns, in order to prevent them from staying behind the progress of the Information Society. The Andalusian regional Government aimed to deploy a network capable of accessing most of the municipalities in the region, even those municipalities that could not be profitable from a monetary perspective. We developed a nonlinear mathematical programming model with special focus on the investment costs. The costs included the parts corresponding to the civil-engineering works, as well as those related to the telematic link deployment. The solution of such a complex problem was found by a genetic algorithm, which was previously tested with a set of trial problems. The results were used to persuade private companies to expand their fiber-optic networks to reach small towns

Kaluza-Klein description of geometric phases in graphene

In this paper, we use the Kaluza-Klein approach to describe topological defects in a graphene layer. Using this approach, we propose a geometric model allowing to discuss the quantum flux in $K$-spin subspace. Within this model, the graphene layer with a topological defect is described by a four-dimensional metric, where the deformation produced by the topological defect is introduced via the three-dimensional part of metric tensor, while an Abelian gauge field is introduced via an extra dimension. We use this new geometric model to discuss the arising of topological quantum phases in a graphene layer with a topological defect.Comment: 16 pages, version accepted to Annals of Physic

Marginal Fermi liquid behavior from 2d Coulomb interaction

A full, nonperturbative renormalization group analysis of interacting electrons in a graphite layer is performed, in order to investigate the deviations from Fermi liquid theory that have been observed in the experimental measures of a linear quasiparticle decay rate in graphite. The electrons are coupled through Coulomb interactions, which remain unscreened due to the semimetallic character of the layer. We show that the model flows towards the noninteracting fixed-point for the whole range of couplings, with logarithmic corrections which signal the marginal character of the interaction separating Fermi liquid and non-Fermi liquid regimes.Comment: 7 pages, 2 Postscript figure

Deformation of the Fermi surface in the extended Hubbard model

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the t-t'-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that exchange interactions V enhance small anisotropies producing deformations of the Fermi surface which break the point group symmetry of the square lattice at the Van Hove filling. This Pomeranchuck instability competes with ferromagnetism and is suppressed at a critical value of U(V). The interaction V renormalizes the t' parameter to smaller values what favours nesting. It also induces changes on the topology of the Fermi surface which can go from hole to electron-like what may explain recent ARPES experiments.Comment: 5 pages, 4 ps figure

Electronic interactions in fullerene spheres

The electron-phonon and Coulomb interactions inC$_{60}$, and larger fullerene spheres are analyzed. The coupling between electrons and intramolecular vibrations give corrections $\sim 1 - 10$ meV to the electronic energies for C$_{60}$, and scales as $R^{-4}$ in larger molecules. The energies associated with electrostatic interactions are of order $\sim 1 - 4$ eV, in C$_{60}$ and scale as $R^{-1}$. Charged fullerenes show enhanced electron-phonon coupling, $\sim 10$ meV, which scales as $R^{-2}$. Finally, it is argued that non only C$_{60}^{-}$, but also C$_{60}^{--}$ are highly polarizable molecules. The polarizabilities scale as $R^3$ and $R^4$, respectively. The role of this large polarizability in mediating intermolecular interactions is also discussed.Comment: 12 pages. No figure