Electron Correlations in Bilayer Graphene

The nature of electron correlations in bilayer graphene has been investigated. An analytic expression for the radial distribution function is derived for an ideal electron gas and the corresponding static structure factor is evaluated. We also estimate the interaction energy of this system. In particular, the functional form of the pair-correlation function was found to be almost insensitive to the electron density in the experimentally accessible range. The inter-layer bias potential also has a negligible effect on the pair-correlation function. Our results offer valuable insights into the general behavior of the correlated systems and serve as an essential starting-point for investigation of the fully-interacting system.Comment: 4 pages, 3 figure

Universal finite size corrections and the central charge in non solvable Ising models

We investigate a non solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength \lambda. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all 0<\lambda<\lambda_0 and \lambda_0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.Comment: 43 pages, 1 figur

Theory of water and charged liquid bridges

The phenomena of liquid bridge formation due to an applied electric field is investigated. A new solution for the charged catenary is presented which allows to determine the static and dynamical stability conditions where charged liquid bridges are possible. The creeping height, the bridge radius and length as well as the shape of the bridge is calculated showing an asymmetric profile in agreement with observations. The flow profile is calculated from the Navier Stokes equation leading to a mean velocity which combines charge transport with neutral mass flow and which describes recent experiments on water bridges.Comment: 10 pages 12 figures, misprints corrected, assumptions more transparen

Response properties of III-V dilute magnetic semiconductors: interplay of disorder, dynamical electron-electron interactions and band-structure effects

A theory of the electronic response in spin and charge disordered media is developed with the particular aim to describe III-V dilute magnetic semiconductors like GaMnAs. The theory combines a detailed k.p description of the valence band, in which the itinerant carriers are assumed to reside, with first-principles calculations of disorder contributions using an equation-of-motion approach for the current response function. A fully dynamic treatment of electron-electron interaction is achieved by means of time-dependent density functional theory. It is found that collective excitations within the valence band significantly increase the carrier relaxation rate by providing effective channels for momentum relaxation. This modification of the relaxation rate, however, only has a minor impact on the infrared optical conductivity in GaMnAs, which is mostly determined by the details of the valence band structure and found to be in agreement with experiment.Comment: 15 pages, 9 figure

Pattern formation in systems with competing interactions

There is a growing interest, inspired by advances in technology, in the low temperature physics of thin films. These quasi-2D systems show a wide range of ordering effects including formation of striped states, reorientation transitions, bubble formation in strong magnetic fields, etc. The origins of these phenomena are, in many cases, traced to competition between short ranged exchange ferromagnetic interactions, favoring a homogeneous ordered state, and the long ranged dipole-dipole interaction, which opposes such ordering on the scale of the whole sample. The present theoretical understanding of these phenomena is based on a combination of variational methods and a variety of approximations, e.g., mean-field and spin-wave theory. The comparison between the predictions of these approximate methods and the results of MonteCarlo simulations are often difficult because of the slow relaxation dynamics associated with the long-range nature of the dipole-dipole interactions. In this note we will review recent work where we prove existence of periodic structures in some lattice and continuum model systems with competing interactions. The continuum models have also been used to describe micromagnets, diblock polymers, etc.Comment: 11 pages, 1 figure, to appear in the AIP conference proceedings of the 10th Granada Seminar on Computational Physics, Sept. 15-19, 2008. (v2) Updated reference

Effect of nonhomogenous dielectric background on the plasmon modes in graphene double-layer structures at finite temperatures

We have calculated the plasmon modes in graphene double layer structures at finite temperatures, taking into account the inhomogeneity of the dielectric background of the system. The effective dielectric function is obtained from the solution of the Poisson equation of three-layer dielectric medium with the graphene sheets located at the interfaces, separating the different materials. Due to the momentum dispersion of the effective dielectric function, the intra- and inter-layer bare Coulomb interactions in the graphene double layer system acquires an additional momentum dependence--an effect that is of the order of the inter-layer interaction itself. We show that the energies of the in-phase and out-of-phase plasmon modes are determined largely by different values of the spatially dependent effective dielectric function. The effect of the dielectric inhomogeneity increases with temperature and even at high temperatures the energy shift induced by the dielectric inhomogeneity and temperature itself remains larger than the broadening of the plasmon energy dispersions due to the Landau damping. The obtained new features of the plasmon dispersions can be observed in frictional drag measurements and in inelastic light scattering and electron energy-loss spectroscopies.Comment: 5 pages, 3 figure

Recurrence Quantification Analysis and Principal Components in the Detection of Short Complex Signals

Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence quantification analysis with principal components analysis to allow for a probabilistic evaluation for the presence of deterministic signals in relatively short data lengths.Comment: 10 pages, 3 figures; Elsevier preprint, elsart style; programs used for analysis available for download at http://homepages.luc.edu/~cwebbe

Fractional Lindstedt series

The parametric equations of the surfaces on which highly resonant quasi-periodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the perturbation parameter, i.e. they are not analytic functions of the perturbation parameter. However rather generally quasi-periodic motions whose frequencies satisfy only one rational relation ("resonances of order 1") admit formal perturbation expansions in terms of a fractional power of the perturbation parameter, depending on the degeneration of the resonance. We find conditions for this to happen, and in such a case we prove that the formal expansion is convergent after suitable resummation.Comment: 40 pages, 6 figure

Modulated phases of a 1D sharp interface model in a magnetic field

We investigate the ground states of 1D continuum models having short-range ferromagnetic type interactions and a wide class of competing longer-range antiferromagnetic type interactions. The model is defined in terms of an energy functional, which can be thought of as the Hamiltonian of a coarse-grained microscopic system or as a mesoscopic free energy functional describing various materials. We prove that the ground state is simple periodic whatever the prescribed total magnetization might be. Previous studies of this model of frustrated systems assumed this simple periodicity but, as in many examples in condensed matter physics, it is neither obvious nor always true that ground states do not have a more complicated, or even chaotic structure.Comment: 12 pages, 3 figure

Unified hydrodynamics theory of the lowest Landau level

We propose a hydrodynamics theory of collective quantum Hall states, which describes incompressible liquids, hexatic liquid crystals, a bubble solid and a Wigner crystal states within a unified framework. The structure of the theory is uniquely determined by the space-time symmetry, and a symmetry with respect to static shear deformations. In agreement with recent experiments the theory predicts two gapped collective modes for incompressible liquids. We argue that the presence of the above two modes is a universal property of a magnetized two-dimensional collective liquid.Comment: RevTex, 8 pages. Revised and expanded versio