Vitor M. Pereira

Tight-binding approach to uniaxial strain in graphene

We analyze the effect of tensional strain in the electronic structure of graphene. In the absence of electron-electron interactions, within linear elasticity theory, and a tight-binding approach, we observe that strain can generate a bulk spectral gap. However, this gap is critical, requiring threshold deformations in excess of 20% and only along preferred directions with respect to the underlying lattice. The gapless Dirac spectrum is robust for small and moderate deformations and the gap appears as a consequence of the merging of the two inequivalent Dirac points only under considerable deformations of the lattice. We discuss how strain-induced anisotropy and local deformations can be used as a means to affect transport characteristics and pinch off current flow in graphene devices.

Strain engineering of graphene's electronic structure.

We propose a route to all-graphene integrated electronic devices by exploring the influence of strain on the electronic structure of graphene. We show that strain can be easily tailored to generate electron beam collimation, 1D channels, surface states and confinement, the basic elements for allgraphene electronics. In addition this proposal has the advantage that patterning can be made on substrates rather than on the graphene sheet, thereby protecting the integrity of the latter. PACS numbers: 81.05.Uw,85.30.Mn,73.90.+f 1 ar X iv :0 81 0. 45 39 v3 [ co nd -m at .m es -h al l] 1 9 Fe b 20 09 Notwithstanding its atomic thickness, graphene sheets have been shown to accommodate a wealth of remarkable fundamental properties, and to hold sound prospects in the context of a new generation of electronic devices and circuitry [1]. The exciting prospect about graphene is that, not only can we have extremely good conductors, but also most active devices made out of graphene. One of the current difficulties with respect to this lies in that conventional electronic operations require the ability to completely pinch-off the charge transport on demand. Although the electric field effect is impressive in graphene [2], the existence of a minimum of conductivity poses a serious obstacle towards desirable on/off ratios. A gapped spectrum would certainly be instrumental. The presence of a gap is implicitly related to the problem of electron confinement, which for Dirac fermions is not easily achievable by conventional means (like electrostatic potential wells) [3]. Geometrical confinement has been achieved in graphene ribbons and dots [4, 5], but the sensitivity of transport to the edge profile [6], and the inherent difficulty in the fabrication of such microstructures with sharply defined edges remains a problem. The ultimate goal would be an all-graphene circuit. This could be achieved by taking a graphene sheet and patterning the different devices and leads by means of appropriate cuts that would generate leads ribbons, dots, etc.. This papercutting electronics can have serious limitations with respect to reliability, scalability, and is prone to damaging and inducing disorder in the graphene sheet [7]. Therefore, in keeping with the paper art analogy, we propose an alternative origami electronics [8]. We show here that all the characteristics of graphene ribbons and dots (viz. geometrical quantization, 1D channels, surface modes) might be locally obtained by patterning, not graphene, but the substrate on which it rests. The essential aspect of our approach is the generation of strain in the graphene lattice capable of changing the in-plane hopping amplitude in an anisotropic way. This can be achieved by means of appropriate geometrical patterns in an homogeneous substrate (grooves, creases, steps or wells), or by means of an heterogeneous substrate in which different regions interact differently with the graphene sheet, generating different strain profiles [Fig. 1(b)]. Another design alternative consists in depositing graphene onto substrates with regions that can be controlably strained on demand [9]. Through a combination of folding and/or clamping a graphene sheet onto such substrate patterns, one might generate local strain profiles suitable for the applications discussed in detail below, while preserving a whole graphene sheet.

Electron-Electron Interactions in Graphene: Current Status and Perspectives

We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant.

Disorder Induced Localized States in Graphene

We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results also have relevance for the problem of disorder in d-wave superconductors.

Modeling disorder in graphene

We present a study of different models of local disorder in graphene. Our focus is on the main effects that vacancies (random, compensated, and uncompensated), local impurities, and substitutional impurities bring into the electronic structure of graphene. By exploring these types of disorder and their connections, we show that they introduce dramatic changes in the low energy spectrum of graphene, viz., localized zero modes, strong resonances, gap and pseudogap behaviors, and nondispersive midgap zero modes.

Geometry, mechanics, and electronics of singular structures and wrinkles in graphene.

As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity, and electronics at the limits of their validity. We describe the transport and electronic structure in the neighborhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene. We use a combination of atomistic mechanical simulations, analytical geometry, and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport, and mobility in suspended samples, and how the geometry-generated pseudomagnetic and pseudoelectric fields might disrupt Landau quantization.

Coulomb Impurity Problem in Graphene

We address the problem of an unscreened Coulomb charge in graphene and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done nonperturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice and (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation: namely, bound state formation and strong renormalization of the van Hove singularities.

Strained graphene: tight-binding and density functional calculations

We determine the band structure of graphene under strain using density functional calculations. The ab initio band structure is then used to extract the best fit to the tight-binding hopping parameters used in a recent microscopic model of strained graphene. It is found that the hopping parameters may increase or decrease upon increasing strain, depending on the orientation of the applied stress. The fitted values are compared with an available parameterization for the dependence of the orbital overlap on the distance separating the two carbon atoms. It is also found that strain does not induce a gap in graphene, at least for deformations up to 10%.

Optical properties of strained graphene

The optical conductivity of graphene strained uniaxially is studied within the Kubo-Greenwood formalism. Focusing on inter-band absorption, we analyze and quantify the breakdown of universal transparency in the visible region of the spectrum, and analytically characterize the transparency as a function of strain and polarization. Measuring transmittance as a function of incident polarization directly reflects the magnitude and direction of strain. Moreover, direction-dependent selection rules permit the identification of the lattice orientation by monitoring the van Hove transitions. These photoelastic effects in graphene can be explored towards atomically thin, broadband optical elements.

Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

A.F. acknowledges FCT Grant No. SFRH/BPD/65600/2009. N.M.R.P. acknowledges Fundos FEDER, through the Programa Operacional Factores de Competitividade-COMPETE and by FCT under Project No. Past-C/FIS/UI0607/2011. A.H.C.N. acknowledges support from DOE Grant No. DE-FG02-08ER46512 and ONR Grant No. MURI N00014-09-1-1063.