T. Stauber

Fine structure constant defines visual transparency of graphene.

We show that the optical transparency of suspended graphene is defined by the fine structure constant, α = e/hc, the parameter that describes coupling between light and relativistic electrons and is traditionally associated with quantum electrodynamics rather than condensed matter physics. Despite being only one atom thick, graphene is found to absorb a significant (πα =2.3%) fraction of incident white light, which is a consequence of graphene’s unique electronic structure. This value translates directly into universal dynamic conductivity G =e/4h within a few % accuracy.There are few phenomena in condensed matter physics that are defined only by the fundamental constants and do not depend on material parameters. Examples are the resistivity quantum, h/e2 (h is Plancks constant and e the electron charge), that appears in a variety of transport experiments and the magnetic flux quantum, h/e, playing an important role in the physics of superconductivity. By and large, sophisticated facilities and special measurement conditions are required to observe any of these phenomena. We show that the opacity of suspended graphene is defined solely by the fine structure constant, a = e2/hc � 1/137 (where c is the speed of light), the parameter that describes coupling between light and relativistic electrons and that is traditionally associated with quantum electrodynamics rather than materials science. Despite being only one atom thick, graphene is found to absorb a significant (pa = 2.3%) fraction of incident white light, a consequence of graphenes unique electronic structure.

Dynamical polarization of graphene at finite doping

The polarization of graphene is calculated exactly within the random phase approximation for arbitrary frequency, wavevector and doping. At finite doping, the static susceptibility saturates to a constant value for low momenta. At q = 2kF 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 ? 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.

Optical conductivity of graphene in the visible region of the spectrum

We compute the optical conductivity of graphene beyond the usual Dirac-cone approximation, giving results that are valid in the visible region of the conductivity spectrum. The effect of next-nearest-neighbor hopping is also discussed. Using the full expression for the optical conductivity, the transmission and reflection coefficients are given. We find that even in the optical regime the corrections to the Dirac-cone approximation are surprisingly small a few percent. Our results help in the interpretation of the experimental results reported by Nair et al. Science 320, 1308 2008.

Electronic transport in graphene: A semiclassical approach including midgap states

Using the semi-classical Boltzmann theory, we calculate the conductivity as function of the carrier density. As usually, we include the scattering from charged impurities, but conclude that the estimated impurity density is too low in order to explain the experimentally observed mobilities. We thus propose an additional scattering mechanism involving midgap states which leads to a similar k-dependence of the relaxation time as charged impurities. The new scattering mechanism can account for the experimental findings such as the sublinear behavior of the conductivity versus gate voltage and the increase of the minimal conductivity for clean samples. We also discuss temperature dependent scattering due to acoustic phonons.

Local defects and ferromagnetism in graphene layers

We study the changes in the electronic structure induced by lattice defects in graphene planes. In many cases, lattice distortions give rise to localized states at the Fermi level. Electron-electron interactions lead to the existence of local moments. The RKKY interaction between these moments is always ferromagnetic, due to the semimetallic properties of graphene.

Efficient graphene-based photodetector with two cavities

We present an efficient graphene-based photodetector with two Fabri-Perot cavities. It is shown that the absorption can reach almost 100% around a given frequency, which is determined by the two-cavity lengths. It is also shown that hysteresis in the absorbance is possible, with the transmittance amplitude of the mirrors working as an external driving field. The role of non-linear contributions to the optical susceptibility of graphene is discussed.

Fluorescence quenching in graphene: A fundamental ruler and evidence for transverse plasmons

This work has been supported by FCT under Grant No. PTDC/FIS/101434/2008 and MIC under Grant No. FIS2010- 21883-C02-02

Conductivity of suspended and non-suspended graphene at finite gate voltage

We compute the DC and the optical conductivity of graphene for finite values of the chemical potential by taking into account the effect of disorder, due to mid-gap states (unitary scatterers) and charged impurities, and the effect of both optical and acoustic phonons. The disorder due to mid-gap states is treated in the coherent potential approximation (CPA, a self-consistent approach based on the Dyson equation), whereas that due to charged impurities is also treated via the Dyson equation, with the self-energy computed using second order perturbation theory. The effect of the phonons is also included via the Dyson equation, with the self energy computed using first order perturbation theory. The self-energy due to phonons is computed both using the bare electronic Greens function and the full electronic Greens function, although we show that the effect of disorder on the phonon-propagator is negligible. Our results are in qualitative agreement with recent experiments. Quantitative agreement could be obtained if one assumes water molelcules under the graphene substrate. We also comment on the electron-hole asymmetry observed in the DC conductivity of suspended graphene.

Phenomenological study of the electronic transport coefficients of graphene

Instituto de Ciencia de Materiales de Madrid. CSIC. Cantoblanco. E-28049 Madrid, Spain(Dated: February 2, 2008)Using a semi-classical approach and input from experiments on the conductivity of graphene, wedetermine the electronic density dependence of the electronic transport coefficients – conductivity,thermal conductivity and thermopower – of doped graphene. Also the electronic density dependenceof the optical conductivity is obtained. Finally we show that the classical Hall effect (low field) ingraphene has the same form as for the independent electron case, characterized by a parabolicdispersion, as long as the relaxation time is proportional to the momentum.

Low-Density Ferromagnetism in Biased Bilayer Graphene

We compute the phase diagram of a biased graphene bilayer. The existence of a ferromagnetic phase is discussed with respect to both carrier density and temperature. We find that the ferromagnetic transition is first-order, lowering the value of U relatively to the usual Stoner criterion. We show that in the ferromagnetic phase the two planes have unequal magnetization and that the electronic density is holelike in one plane and electronlike in the other.