J. M. B. Lopes dos Santos

Biased bilayer graphene: Semiconductor with a gap tunable by the electric field effect

We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magnetotransport data (Shubnikov-de Haas measurements of the cyclotron mass), and using a tight-binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to midinfrared energies by using fields of less, approximately < 1 V/nm, below the electric breakdown of SiO2. The opening of a gap is clearly seen in the quantum Hall regime.

Graphene bilayer with a twist: electronic structure.

We consider a graphene bilayer with a relative small angle rotation between the layers--a stacking defect often seen in the surface of graphite--and calculate the electronic structure near zero energy in a continuum approximation. Contrary to what happens in an AB stacked bilayer and in accord with observations in epitaxial graphene, we find: (a) the low energy dispersion is linear, as in a single layer, but the Fermi velocity can be significantly smaller than the single-layer value; (b) an external electric field, perpendicular to the layers, does not open an electronic gap.

Observation of Van Hove singularities in twisted graphene layers

When a Van Hove singularity exists near the Fermi energy of a solid’s density of states, it can cause a variety of exotic phenomena to emerge. Scanning tunnelling microscope measurements indicate that when graphite’s graphene sheets are rotated out of their usual alignment, it can generate low-energy Van Hove singularities for which the position is controlled by the angle of rotation.

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.

Localized States at Zigzag Edges of Bilayer Graphene

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.

Zigzag graphene nanoribbon edge reconstruction with Stone-Wales defects

tight-binding method, with parameters determined by ab-initio calculations of very narrow ribbons. We explore the characteristics of the electronic band structure with a focus on the nature of edge states. Edge reconstruction allows the appearance of a new type of egde states. They are dispersive, with non-zero amplitudes in both sub-lattices; furthermore, the amplitudes have two components that decrease with dierent decay lengths with the distance from the edge; at the Dirac points one of these lengths diverges, whereas the other remains nite, of the order of the lattice parameter. We trace this curious eect to the doubling of the unit cell along the edge, brought about by the edge reconstruction. In the presence of a magnetic eld, the zero-energy Landau level is no longer degenerate with edge states as in the case of pristine zigzag ribbon.

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.

Electron waves in chemically substituted graphene

We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential as well as in the hopping amplitude. We employ a T-matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity that can be understood in terms of bound, semi-bound, and unbound processes for the Dirac electrons. These interference effects can be detected by scanning tunneling microscopy.

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. We show that due to the formation of sub-bands in the ribbons it is possible to spatially localize some of the electronic modes using a p-n-p junction. We also show that scattering of confined Dirac electrons in a narrow channel by an infinitely massive wall induces mode mixing, giving a qualitative reason for the fact that an analytical solution to the spectrum of Dirac electrons confined in a square box has not yet been found. A first attempt to solve this problem is presented. We find that only the trivial case k = 0 has a solution that does not require the existence of evanescent modes. We also study the spectrum of quantum dots of graphene in a perpendicular magnetic field. This problem is studied in the Dirac approximation, and its solution requires a numerical method whose details are given. The formation of Landau levels in the dot is discussed. The inclusion of the Coulomb interaction among the electrons is considered at the self-consistent Hartree level, taking into account the interaction with an image charge density necessary to keep the back-gate electrode at zero potential. The effect of a radial confining potential is discussed. The density of states of circular and hexagonal quantum dots, described by the full tight-binding model, is studied using the Lanczos algorithm. This is necessary to access the detailed shape of the density of states close to the Dirac point when one studies large systems. Our study reveals that zero-energy edge states are also present in graphene quantum dots. Our results are relevant for experimental research in graphene nanostructures. The style of writing is pedagogical, in the hope that newcomers to the subject will find this paper a good starting point for their research.