Coulomb Interactions and Ferromagnetism in Pure and Doped Graphene

We study the presence of ferromagnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and doping. We show that exchange interactions between Dirac fermions can stabilize a ferromagnetic phase at low doping when the coupling is sufficiently large. In clean systems, the zero temperature phase diagram shows both first order and second order transition lines and two distinct ferromagnetic phases: one phase with only one type of carriers (either electrons or holes) and another with two types of carriers (electrons and holes). Using the coherent phase approximation (CPA) we argue that disorder further stabilizes the ferromagnetic phase.Comment: 10 pages; published versio

Wyman's solution, self-similarity and critical behaviour

We show that the Wyman's solution may be obtained from the four-dimensional Einstein's equations for a spherically symmetric, minimally coupled, massless scalar field by using the continuous self-similarity of those equations. The Wyman's solution depends on two parameters, the mass $M$ and the scalar charge $\Sigma$. If one fixes $M$ to a positive value, say $M_0$, and let $\Sigma^2$ take values along the real line we show that this solution exhibits critical behaviour. For $\Sigma^2 >0$ the space-times have eternal naked singularities, for $\Sigma^2 =0$ one has a Schwarzschild black hole of mass $M_0$ and finally for $-M_0^2 \leq \Sigma^2 < 0$ one has eternal bouncing solutions.Comment: Revtex version, 15pages, 6 figure

Conductance quantization in mesoscopic graphene

Using a generalized Landauer approach we study the non-linear transport in mesoscopic graphene with zig-zag and armchair edges. We find that for clean systems, the low-bias low-temperature conductance, G, of an armchair edge system in quantized as G/t=4 n e^2/h, whereas for a zig-zag edge the quantization changes to G/t t=4(n+1/2)e^2/h, where t is the transmission probability and n is an integer. We also study the effects of a non-zero bias, temperature, and magnetic field on the conductance. The magnetic field dependence of the quantization plateaus in these systems is somewhat different from the one found in the two-dimensional electron gas due to a different Landau level quantization.Comment: 6 pages, 9 figures. Final version published in Physical Review

Quantum Cosmology in Scalar-Tensor Theories With Non Minimal Coupling

Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form, which corresponds to the minimal coupling case, whose general solution is known. Performing the inverse conformal transformation in the solution so found, we can construct the corresponding one in the original frame. This procedure can also be employed with the bohmian trajectories. In this way, we can study the classical limit of some solutions of this quantum model. While the classical limit of these solutions occurs for small scale factors in the Einstein's frame, it happens for small values of the scalar field non minimally coupled to gravity in the Jordan's frame, which includes large scale factors.Comment: latex, 18 page

Electronic properties of graphene multilayers

We study the effects of disorder in the electronic properties of graphene multilayers, with special focus on the bilayer and the infinite stack. At low energies and long wavelengths, the electronic self-energies and density of states exhibit behavior with divergences near half-filling. As a consequence, the spectral functions and conductivities do not follow Landau's Fermi liquid theory. In particular, we show that the quasiparticle decay rate has a minimum as a function of energy, there is a universal minimum value for the in-plane conductivity of order e^2/h per plane and, unexpectedly, the c-axis conductivity is enhanced by disorder at low doping, leading to an enormous conductivity anisotropy at low temperatures.Comment: 4 pages, 4 figure. Reference to exciting new ARPES results on graphite added (we thank A. Lanzara for sharing the paper prior to its publication

Dirac Fermion Confinement in Graphene

We study the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magnetic field B. We show, analytically and numerically, that confinement leads to anomalies in the electronic spectrum and to a magnetic field dependent crossover from \sqrt{B}, characteristic of Dirac-Landau level behavior, to linear in B behavior, characteristic of confinement. This crossover occurs when the radius of the Landau level becomes of the order of the width of the system. As a result, we show that the Shubnikov-de Haas oscillations also change as a function of field, and lead to a singular Landau plot. We show that our theory is in excellent agreement with the experimental data.Comment: 4 pages, 6 figure