Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model

To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight.Comment: 25 pages, 10 figure

On the universal AC optical background in graphene

The latest experiments have confirmed the theoretically expected universal value $\pi e^2/2h$ of the ac conductivity of graphene and have revealed departures of the quasiparticle dynamics from predictions for the Dirac fermions in idealized graphene. We present analytical expressions for the ac conductivity in graphene which allow one to study how it is affected by interactions, temperature, external magnetic field and the opening of a gap in the quasiparticle spectrum. We show that the ac conductivity of graphene does not necessarily give a metrologically accurate value of the von Klitzing constant $h/e^2$, because it is depleted by the electron-phonon interaction. In a weak magnetic field the ac conductivity oscillates around the universal value and the Drude peak evolves into a peak at the cyclotron frequency.Comment: 18 pages, 4 figures; v2: to match New J. Phys. (Focus on Graphene issue

Effect of Holstein phonons on the electronic properties of graphene

We obtain the self-energy of the electronic propagator due to the presence of Holstein polarons within the first Born approximation. This leads to a renormalization of the Fermi velocity of one percent. We further compute the optical conductivity of the system at the Dirac point and at finite doping within the Kubo-formula. We argue that the effects due to Holstein phonons are negligible and that the Boltzmann approach which does not include inter-band transition and can thus not treat optical phonons due to their high energy of $\hbar\omega_0\sim0.1-0.2$eV, remains valid.Comment: 13 pages, 4 figure

Time-averaged copper concentrations from continuous exposures predicts pulsed exposure toxicity to the marine diatom, Phaeodactylum tricornutum: importance of uptake and elimination

Intermittent, fluctuating and pulsed contaminant discharges result in organisms receiving highly variable contaminant exposures. Current water quality guidelines are predominantly derived using data from continuous exposure toxicity tests, and most frequently applied by regulators with the assumption that concentrations from a single sampling event will provide a meaningful approach to assessing potential effects. This study investigated the effect of single and multiple (daily) dissolved copper pulses on the marine diatom, Phaeodactylum tricornutum, including measurements of copper uptake and elimination to investigate the toxic mechanism. Copper pulses of between 0.5 and 24 h and continuous exposures with equivalent 72-h time-averaged concentrations (TACs) resulted in similar biomass inhibition of P. tricornutum, with continuous exposures often being marginally more toxic. Rates of cell division generally recovered to control levels within 24 h of the copper pulse removal. Upon resuspension in clean seawater, the extracellular copper per cell decreased rapidly, whereas the intracellular copper per cell decreased slowly. Negligible loss of copper from the total algal biomass indicated that P. tricornutum did not have an effective mechanism for eliminating copper from cells, rather the intracellular copper decreased as a result of dilution by cellular division as the algal growth rate recovered. The measurement of copper uptake after 72-h exposure and kinetics of elimination thereafter suggest that continuous exposures are marginally more toxic to P. tricornutum than pulsed copper exposures with equivalent TACs because slow internalization and saturation of algal membrane transport sites results in less copper uptake into pulse-exposed cells than continuously-exposed cells coupled with dilution of internalized copper via cellular division in the post-exposure period. In the case of P. tricornutum, the results indicate that water quality guidelines for copper based on continuous exposure will be conservative when applied to short-term discharges

Tomonaga-Luttinger model with an impurity for a weak two-body interaction

The Tomonaga-Luttinger model with impurity is studied by means of flow equations for Hamiltonians. The system is formulated within collective density fluctuations but no use of the bosonization formula is made. The truncation scheme includes operators consisting of up to four fermion operators and is valid for small electron-electron interactions. In this regime, the exact expression for the anomalous dimension is recovered. Furthermore, we verify the phase diagram of Kane and Fisher also for intermediate impurity strength. The approach can be extended to more general one-body potentials.Comment: 10 pages, 1 figur

Dynamical polarization of graphene at finite doping

The polarization of graphene is calculated exactly within the random phase approximation for arbitrary frequency, wave vector, and doping. At finite doping, the static susceptibility saturates to a constant value for low momenta. At $q=2 k_{F}$ it has a discontinuity only in the second derivative. In the presence of a charged impurity this results in Friedel oscillations which decay with the same power law as the Thomas Fermi contribution, the latter being always dominant. The spin density oscillations in the presence of a magnetic impurity are also calculated. The dynamical polarization for low $q$ and arbitrary $\omega$ is employed to calculate the dispersion relation and the decay rate of plasmons and acoustic phonons as a function of doping. The low screening of graphene, combined with the absence of a gap, leads to a significant stiffening of the longitudinal acoustic lattice vibrations.Comment: 17 pages, 6 figures, 1 tabl

Plasmons in layered structures including graphene

We investigate the optical properties of layered structures with graphene at the interface for arbitrary linear polarization at finite temperature including full retardation by working in the Weyl gauge. As a special case, we obtain the full response and the related dielectric function of a layered structure with two interfaces. We apply our results to discuss the longitudinal plasmon spectrum of several single and double layer devices such as systems with finite and zero electronic densities. We further show that a nonhomogeneous dielectric background can shift the relative weight of the in-phase and out-of-phase mode and discuss how the plasmonic mode of the upper layer can be tuned into an acoustic mode with specific sound velocity.Comment: 18 pages, 6 figure

Resonant Visible Light Modulation with Graphene

Fast modulation and switching of light at visible and near-infrared (vis-NIR) frequencies is of utmost importance for optical signal processing and sensing technologies. No fundamental limit appears to prevent us from designing wavelength-sized devices capable of controlling the light phase and intensity at gigaherts (and even terahertz) speeds in those spectral ranges. However, this problem remains largely unsolved, despite recent advances in the use of quantum wells and phase-change materials for that purpose. Here, we explore an alternative solution based upon the remarkable electro-optical properties of graphene. In particular, we predict unity-order changes in the transmission and absorption of vis-NIR light produced upon electrical doping of graphene sheets coupled to realistically engineered optical cavities. The light intensity is enhanced at the graphene plane, and so is its absorption, which can be switched and modulated via Pauli blocking through varying the level of doping. Specifically, we explore dielectric planar cavities operating under either tunneling or Fabry-Perot resonant transmission conditions, as well as Mie modes in silicon nanospheres and lattice resonances in metal particle arrays. Our simulations reveal absolute variations in transmission exceeding 90% as well as an extinction ratio >15 dB with small insertion losses using feasible material parameters, thus supporting the application of graphene in fast electro-optics at vis-NIR frequencies.Comment: 17 pages, 13 figures, 54 reference

Dirac electrons in graphene-based quantum wires and quantum dots

In this paper we analyse the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots made of graphene.Comment: Contribution for J. Phys.: Cond. Mat. special issue on graphene physic