Variational approach to the excitonic phase transition in graphene

We analyze the Coulomb interacting problem in undoped graphene layers by using an excitonic variational ansatz. By minimizing the energy, we derive a gap equation which reproduces and extends known results. We show that a full treatment of the exchange term, which includes the renormalization of the Fermi velocity, tends to suppress the phase transition by increasing the critical coupling at which the excitonic instability takes place.Comment: 4 page

Electron-induced rippling in graphene

We show that the interaction between flexural phonons, when corrected by the exchange of electron-hole excitations, may place the graphene sheet very close to a quantum critical point characterized by the strong suppression of the bending rigidity of the membrane. Ripples arise then due to spontaneous symmetry breaking, following a mechanism similar to that responsible for the condensation of the Higgs field in relativistic field theories. In the presence of membrane tensions, ripple condensation may be reinforced or suppressed depending on the sign of the tension, following a zero-temperature buckling transition in which the order parameter is given essentially by the square of the gradient of the flexural phonon field.Comment: 4 pages, 3 figure

Renormalization group analysis of electrons near a Van Hove singularity.

A model of interacting two dimensional electrons near a Van Hove singularity is studied, using renormalization group techniques. In hole doped systems, the chemical potential is found to be pinned near the singularity, when the electron-electron interactions are repulsive. The RG treatment of the leading divergences appearing in perturbation theory give rise to marginal behavior and anisotropic superconductivity.Comment: 4 Latex pages + 5 postcript figure

Electrostatic screening in fullerene molecules

The screening properties of fullerene molecules are described by means of a continuum model which uses the electronic wavefunctions of planar graphite as a starting point. The long distance behavior of the system gives rise to a renormalizable theory, which flows towards a non trivial fixed point. Its existence implies an anomalous dielectric constant. The screening properties are neither metallic nor insulating. Alternatively, the intramolecular screening is obtained from a simple approximation to the electronic wavefunctions. Intermolecular effects are also calculated. As a consistency check, it is shown that the observed polarizability of C$_{60}$ is well eproduced.Comment: 7 pages. Revte

Charge distribution and screening in layered graphene systems

The charge distribution induced by external fields in finite stacks of graphene planes, or in semiinfinite graphite is considered. The interlayer electronic hybridization is described by a nearest neighbor hopping term, and the charge induced by the self consistent electrostatic potential is calculated within linear response (RPA). The screening properties are determined by contributions from inter- and intraband electronic transitions. In neutral systems, only interband transitions contribute to the charge polarizability, leading to insulating-like screening properties, and to oscillations in the induced charge, with a period equal to the interlayer spacing. In doped systems, we find a screening length equivalent to 2-3 graphene layers, superimposed to significant charge oscillations.Comment: 8 page