Showing papers by "Nuno M. R. Peres published in 2008"
TL;DR: It is shown 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.
Abstract: 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 Planck's 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 feminine 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 graphene's unique electronic structure.
7,952 citations
TL;DR: In this paper, the optical conductivity of graphene has been computed beyond the usual Dirac-cone approximation, giving results that are valid in the visible region of the conductivity spectrum.
Abstract: 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.
754 citations
TL;DR: In this article, the effects of site dilution disorder on the electronic properties in graphene multilayers, in particular the bilayer and the infinite stack, were studied. And the authors also studied the problem of impurities in the biased graphene bilayer.
Abstract: We study the effects of site dilution disorder on the electronic properties in graphene multilayers, in particular the bilayer and the infinite stack. The simplicity of the model allows for an easy implementation of the coherent-potential approximation and some analytical results. Within the model we compute the self-energies, the density of states, and the spectral functions. Moreover, we obtain the frequency and temperature dependence of the conductivity as well as the dc conductivity. The $c$-axis response is unconventional in the sense that impurities increase the response for low enough doping. We also study the problem of impurities in the biased graphene bilayer.
245 citations
TL;DR: It is shown that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.
Abstract: We examine the conditions necessary for the presence of localized magnetic moments on adatoms with inner shell electrons in graphene. We show that the low density of states at the Dirac point, and the anomalous broadening of the adatom electronic level, lead to the formation of magnetic moments for arbitrarily small local charging energy. As a result, we obtain an anomalous scaling of the boundary separating magnetic and nonmagnetic states. We show that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.
213 citations
TL;DR: In this article, the existence of a ferromagnetic phase is discussed with respect to both carrier density and temperature, and it is shown that the transition is first-order, lowering the value of U relatively to the usual Stoner criterion.
Abstract: 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.
122 citations
TL;DR: It is shown that zero-energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene and (ii) states with a finite amplitude over the two layers, with an enhanced penetration into the bulk.
Abstract: We report the existence of zero-energy surface states localized at zigzag edges of bilayer graphene. Working within the tight-binding approximation we derive the analytic solution for the wave functions of these peculiar surface states. It is shown that zero-energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene and (ii) states with a finite amplitude over the two layers, with an enhanced penetration into the bulk. The bulk and surface (edge) electronic structure of bilayer graphene nanoribbons is also studied, both in the absence and in the presence of a bias voltage between planes.
122 citations
TL;DR: In this paper, the formation of energy gaps in the spectrum of graphene and its bilayer when both these materials are covered with water and ammonia molecules was studied and the energy gaps obtained are within the range 20-30 meV, values compatible to those found in experimental studies of graphene bilayer.
Abstract: In this paper we study the formation of energy gaps in the spectrum of graphene and its bilayer when both these materials are covered with water and ammonia molecules. The energy gaps obtained are within the range 20–30 meV, values compatible to those found in experimental studies of graphene bilayer. We further show that the binding energies are large enough for the adsorption of the molecules to be maintained even at room temperature.
117 citations
TL;DR: In this article, the authors compute the dc and optical conductivity of graphene for finite values of the chemical potential by taking into account the effect of disorder, due to midgap states (unitary scatterers) and charged impurities.
Abstract: 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 midgap states (unitary scatterers) and charged impurities, and the effect of both optical and acoustic phonons. The disorder due to midgap states is treated in the coherent-potential approximation (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 Green's function and the full electronic Green's 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 molecules under the graphene substrate. We also comment on the electron-hole asymmetry observed in the dc conductivity of suspended graphene.
95 citations
TL;DR: In this article, the effect of an external electric field applied perpendicular to the system was investigated, using a parallel plate capacitor model, with screening correction at the Hartree level, and the full tight-binding description was compared with its 4-band and 2-band continuum approximations.
Abstract: We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system -- \emph{biased bilayer}. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its 4-band and 2-band continuum approximations, and the 4-band model is shown to be always a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, either made out of SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point to understand the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, as the second-nearest-neighbor hopping energies $t'$ (in-plane) and $\gamma_{4}$ (inter-layer), and the on-site energy $\Delta$.
84 citations
Journal Article•
TL;DR: It is shown 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.
82 citations
TL;DR: In this article, the self-energy of the electronic propagator due to the presence of Holstein polarons was obtained within the first Born approximation, which leads to a renormalization of the Fermi velocity of 1%.
Abstract: 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 1%. 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 transitions and can thus not treat optical phonons due to their high energy of eV, remains valid.
TL;DR: In this article, the authors studied the tunneling of chiral electrons in graphene through a region where the electronic spectrum changes from the usual linear dispersion to a hyperbolic dispersion, due to the presence of a gap.
Abstract: We study the tunneling of chiral electrons in graphene through a region where the electronic spectrum changes from the usual linear dispersion to a hyperbolic dispersion, due to the presence of a gap. It is shown that, contrary to the tunneling through a potential barrier, the transmission of electrons is, in this case, smaller than one for normal incidence. This mechanism may be useful for designing electronic devices made of graphene.
TL;DR: In this article, the effect of phonons and disorder due to charged impurities and unitary scatterers on the infrared conductivity of graphene at finite chemical potential and temperature was studied.
Abstract: We study the infrared conductivity of graphene at finite chemical potential and temperature taking into account the effect of phonons and disorder due to charged impurities and unitary scatterers, that is, considering all possible single-particle scattering mechanisms. The screening of the long-range Coulomb potential is treated using the random phase approximation coupled to the coherent potential approximation. The effect of the electron-phonon coupling is studied in second-order perturbation theory. The theory has essentially one free parameter, namely, the number of charge impurities per carbon, nCi. Our most important results are the finding of an anomalous enhancement of the conductivity in a frequency region that is blocked by Pauli exclusion, in a picture based on independent electrons, and an impurity broadening of the conductivity threshold, close to twice the chemical potential. We also find that phonons induce Stokes and anti-Stokes lines that produce an excess conductivity, when compared to the far infrared value of σ0=(π/2)e2/h.
TL;DR: In this article, the effect of phonons and disorder due to charged impurities and unitary scatterers on the infrared conductivity of graphene at finite chemical potential and temperature was studied.
Abstract: We study the infrared conductivity of graphene at finite chemical potential and temperature taking into account the effect of phonons and disorder due to charged impurities and unitary scatterers. The screening of the long-range Coulomb potential is treated using the random phase approximation coupled to the coherent potential approximation. The effect of the electron-phonon coupling is studied in second-order perturbation theory. The theory has essentially one free parameter, namely, the number of charge impurities per carbon, n^{{\rm C}}_i. We find an anomalous enhancement of the conductivity in a frequency region that is blocked by Pauli exclusion and an impurity broadening of the conductivity threshold. We also find that phonons induce Stokes and anti-Stokes lines that produce an excess conductivity, when compared to the far infrared value of \sigma_0 = (\pi/2) e^2/h.
TL;DR: In this paper, the conductivity of a clean graphene sheet at finite temperatures was calculated starting from the tight-binding model and a finite value for the dc-conductivity at zero temperature was obtained.
Abstract: We calculate the conductivity of a clean graphene sheet at finite temperatures starting from the tight-binding model. We obtain a finite value for the dc-conductivity at zero temperature. For finite temperature, the spontaneous electron-hole creation, responsible for the finite conductivity at zero temperature, is washed out and the dc-conductivity yields zero. Our results are in agreement with calculations based on the field-theoretical model for graphene.
TL;DR: In this paper, the conductivity of a clean graphene sheet at finite temperatures was calculated starting from the tight-binding model and the authors obtained a finite value for the dc-conductivity at zero temperature.
Abstract: We calculate the conductivity of a clean graphene sheet at finite temperatures starting from the tight-binding model. We obtain a finite value for the dc-conductivity at zero temperature. For finit...
01 Oct 2008
TL;DR: In this paper, the authors use a tight binding approach to study how the gap changes with the applied electric field and show that a gap between zero and mid-infrared energies can be induced and externally tuned in these devices.
Abstract: Bilayer graphene - two coupled single graphene layers stacked as in graphite - provides the only known semiconductor with a gap that can be tuned externally through electric field effect. Here we use a tight binding approach to study how the gap changes with the applied electric field. Within a parallel plate capacitor model and taking into account screening of the external field, we describe real back gated and/or chemically doped bilayer devices. We show that a gap between zero and midinfrared energies can be induced and externally tuned in these devices, making bilayer graphene very appealing from the point of view of applications. However, applications to nanotechnology require careful treatment of the efiect of sample boundaries. This being particularly true in graphene, where the presence of edge states at zero energy - the Fermi level of the undoped system - has been extensively reported. Here we show that also bilayer graphene supports surface states localized at zigzag edges. The presence of two layers, however, allows for a new type of edge state which shows an enhanced penetration into the bulk and gives rise to band crossing phenomenon inside the gap of the biased bilayer system.
TL;DR: In this paper, the wave functions of the edge states of N-layer graphene were derived within the tight-binding approximation, and using the simplest nearest-neighbor model, the analytic solution for the wave function of these peculiar surface states was derived.
Abstract: We report the existence of zero-energy surface states localized at zigzag edges of N-layer graphene. Working within the tight-binding approximation, and using the simplest nearest-neighbor model, we derive the analytic solution for the wave functions of these peculiar surface states. It is shown that zero-energy edge states in multilayer graphene can be divided into three families: i) states living only on a single plane, equivalent to surface states in monolayer graphene; ii) states with finite amplitude over the two last, or the two first layers of the stack, equivalent to surface states in bilayer graphene; iii) states with finite amplitude over three consecutive layers. Multilayer graphene edge states are shown to be robust to the inclusion of the next-nearest-neighbor interlayer hopping. We generalize the edge state solution to the case of graphite steps with zigzag edges, and show that edge states measured through scanning tunneling microscopy and spectroscopy of graphite steps belong to family i) or ii) mentioned above, depending on the way the top layer is cut.
TL;DR: In this paper, the authors report the existence of zero energy surface states localized at zigzag edges of $N$-layer graphene and derive the analytic solution for the wavefunctions of these peculiar surface states.
Abstract: We report the existence of zero energy surface states localized at zigzag edges of $N$-layer graphene. Working within the tight-binding approximation, and using the simplest nearest-neighbor model, we derive the analytic solution for the wavefunctions of these peculiar surface states. It is shown that zero energy edge states in multilayer graphene can be divided into three families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene; (ii) states with finite amplitude over the two last, or the two first layers of the stack, equivalent to surface states in bilayer graphene; (iii) states with finite amplitude over three consecutive layers. Multilayer graphene edge states are shown to be robust to the inclusion of the next nearest-neighbor interlayer hopping. We generalize the edge state solution to the case of graphite steps with zigzag edges, and show that edge states measured through scanning tunneling microscopy and spectroscopy of graphite steps belong to family (i) or (ii) mentioned above, depending on the way the top layer is cut.
TL;DR: In this article, the transmission of an electron through an impurity in polyacene was studied and the scattering problem was reduced to that of two independent chains with an alternating sequence of atoms of two types.
Abstract: We compute the transmission of an electron through an impurity in polyacene. For simplicity the disorder is confined to a single unit cell. When the impurity preserves the inversion symmetry around the central axis, the scattering problem can be reduced to that of two independent chains with an alternating sequence of atoms of two types. An analytical expression for the transmission coefficient is derived. On-site and off-diagonal defects are considered and shown to display very different electron scattering properties.
Posted Content•
TL;DR: In this paper, the edge magnetization of bilayer graphene ribbons with zigzag edges was studied and shown to be ferromagnetic along the edge, involving sites of the two layers, and antiferromagnetic between opposite edges.
Abstract: We study the edge magnetization of bilayer graphene ribbons with zigzag edges. The presence of flat edge-state bands at the Fermi energy of undoped bilayer, which gives rise to a strong peak in the density of states, makes bilayer ribbons magnetic at the edges even for very small on-site electronic repulsion. Working with the Hubbard model in the Hartree Fock approximation we show that the magnetic structure in bilayer ribbons with zigzag edges is ferromagnetic along the edge, involving sites of the two layers, and antiferromagnetic between opposite edges. It is also shown that this magnetic structure is a consequence of the nature of the edge states present in bilayer ribbons with zigzag edges. Analogously to the monolayer case, edge site magnetization as large as $m \approx0.2 \mu_{B}$ (per lattice site) even at small on-site Hubbard repulsion $U \approx 0.3 {eV}$ is realized in nanometer wide bilayer ribbons.
Journal Article•
TL;DR: In this article, the edge magnetization of bilayer graphene ribbons with zigzag edges was studied and shown to be ferromagnetic along the edge, involving sites of the two layers, and antiferromagnetic between opposite edges.
Abstract: We study the edge magnetization of bilayer graphene ribbons with zigzag edges. The presence of flat edge-state bands at the Fermi energy of undoped bilayer, which gives rise to a strong peak in the density of states, makes bilayer ribbons magnetic at the edges even for very small on-site electronic repulsion. Working with the Hubbard model in the Hartree Fock approximation we show that the magnetic structure in bilayer ribbons with zigzag edges is ferromagnetic along the edge, involving sites of the two layers, and antiferromagnetic between opposite edges. It is also shown that this magnetic structure is a consequence of the nature of the edge states present in bilayer ribbons with zigzag edges. Analogously to the monolayer case, edge site magnetization as large as m≈0.2 μΒ (per lattice site) even at small on-site Hubbard repulsion U≈0.3 eV is realized in nanometer wide ribbons.
TL;DR: In this paper, the phase diagram of a biased graphene bilayer is computed and the existence of a ferromagnetic phase is discussed both in the critical on-site interaction $U c$ versus doping density and versus temperature.
Abstract: The phase diagram of a biased graphene bilayer is computed and the existence of a ferromagnetic phase is discussed both in the critical on-site interaction $U_{c}$ versus doping density and versus temperature. We show that in the ferromagnetic phase the two planes have unequal magnetization and that the electronic density is hole like in one plane and electron like in the other. We give evidence for a \emph{first-order} phase transition between paramagnetic and ferromagnetic phases induced by doping at zero temperature.
TL;DR: In this article, the phase diagram of a biased graphene bilayer is computed and the existence of a ferromagnetic phase is discussed both in the critical on-site interaction Uc versus doping density and versus temperature.
Abstract: The phase diagram of a biased graphene bilayer is computed and the existence of a ferromagnetic phase is discussed both in the critical on-site interaction Uc versus doping density and versus temperature. We show that in the ferromagnetic phase the two planes have unequal magnetization and that the electronic density is hole-like in one plane and electron-like in the other. We give evidence for a first-order phase transition between paramagnetic and ferromagnetic phases induced by doping at zero temperature.
14 Jul 2008
TL;DR: In this article, a finite volume method is applied to the three-dimensional simulation of heat transfer of a viscoelastic fluid in laminar flow through a rectangular channel with an aspect ratio of 2 and constant heat flux at the channel walls.
Abstract: A finite‐volume method is applied to the three‐dimensional simulation of heat transfer of a viscoelastic fluid in laminar flow through a rectangular channel with an aspect ratio of 2 and constant heat flux at the channel walls. The objectives of the present work are twofold: (a) to compare the numerical results with the heat transfer experimental data of Hartnett and Kostic [l]; (b) to analyze the influence of the secondary flow on the heat transfer enhancement on account of the non‐zero second normal‐stress difference. The rheology of the viscoelastic fluid is represented by the Phan‐Thien‐Tanner constitutive equation with non‐zero second normal‐stress difference. The simulations show the strong effect of secondary flows on the correct prediction of experimental results. The predictions confirm the enhancement of local and mean Nusselt numbers, as found experimentally by Hartnett and Kostic [1], and show that free convection has a major influence in the experimental heat transfer results for Newtonian fl...
TL;DR: In this paper, the authors studied the tunneling of chiral electrons in graphene through a region where the electronic spectrum changes from the usual linear dispersion to a hyperbolic dispersion, due to the presence of a gap.
Abstract: We study the tunneling of chiral electrons in graphene through a region where the electronic spectrum changes from the usual linear dispersion to a hyperbolic dispersion, due to the presence of a gap. It is shown that contrary to the tunneling through a potential barrier, the transmission of electrons is, in this case, smaller than one for normal incidence. This mechanism may be useful for designing electronic devices made of graphene.
TL;DR: In this article, the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots made of graphene were analyzed and shown to be similar to ours.
Abstract: 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.
01 Jan 2008
TL;DR: In this article, the authors studied the problem of Dirac-Landau convergence in graphene in the presence of a perpendicular magnetic field and showed that the Shubnikov-de Haas oscillations also change as a function of the magnetic field, and lead to a singular Landau plot.
Abstract: Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco E28049 Madrid, Spain(Dated: February 4, 2008)We study the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magneticfield B. We show, analytically and numerically, that confinement le ads to anomalies in the electronic spectrumand to a magnetic field dependent crossover from√B, characteristic of Dirac-Landau level behavior, to linearinB behavior, characteristic of confinement. This crossover oc curs when the radius of the Landau level becomesof the order of the width of the system. As a result, we show that the Shubnikov-de Haas oscillations also changeas a function of field, and lead to a singular Landau plot. We sh ow that our theory is in excellent agreement withthe experimental data.