Spectrum of π\pi-electrons in Graphene As a Macromolecule

We report the exact solution of spectral problem for a graphene sheet framed by two armchair- and two zigzag-shaped boundaries. The solution is found for the $\pi$ electron Hamiltonian and gives, in particular, a closed analytic expression of edge-state energies in graphene. It is shown that the lower symmetry of graphene, in comparison with $C_{6h}$ of 2D graphite, has a profound effect on the graphene band structure. This and other obtained results have far going implications for the understanding of graphene electronics. Some of them are briefly discussed.Comment: Revised in connection with publication in PRL, editin

The Brief History of Russian Obituary

Up to the 1990s, the genre of the obituary was a wide-spread genre of printed media in Russia. From the beginning of the 19th century, the obituary suffered some significant changes and even served as an instrument in different social and political manipulations. Some modern Russian researchers consider that this genre is dying nowadays, but it is not entirely true. Presently, obituaries are still popular in periodicals of small Russian towns and regional centers as well as in designated magazines. This review is aimed at the short description of the history of Russian obituary and its contemporary state. The researcher focuses on the different manners of speaking about the subject of the obituary and his/her characteristics, and on the representation of his/her biography. For this purpose, it is very important to examine the social and historical context of each period when the obituaries have been created. It can be said that the writing of obituaries is a specific practice, the specific social action that puts the death of the most prominent or remarkable person into the public space. Any biographic text is a social utterance and a narrative, designed to conceptualize actual social processes for contemporaries

Spectrum of π\pi Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance

An exact description of $\pi$ electrons based on the tight-binding model of graphene as an alternant, plane macromolecule is presented. The model molecule can contain an arbitrary number of benzene rings and has armchair- and zigzag-shaped edges. This suggests an instructive alternative to the most commonly used approach, where the reference is made to the honeycomb lattice periodic in its A and B sublattices. Several advantages of the macromolecule model are demonstrated. The newly derived analytical relations detail our understanding of $\pi$ electron nature in achiral graphene ribbons and carbon tubes and classify these structures as quantum wires.Comment: 13 pages 8 figures, revised in line with referee's comment

The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation; the results are exact for non-interacting electrons. Our method fully accounts for the effects of the disorder and the periodic modulation, irrespective of their relative strength, as long as Landau level mixing is negligible. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder. This appears to be the relevant regime to understand recent experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multi-channel scattering problems.Comment: 13 pages, 11 figure

Complex-band structure: a method to determine the off-resonant electron transport in oligomers

We validate that off-resonant electron transport across {\it ultra-short} oligomer molecular junctions is characterised by a conductance which decays exponentially with length, and we discuss a method to determine the damping factor via the energy spectrum of a periodic structure as a function of complex wavevector. An exact mapping to the complex wavevector is demonstrated by first-principle-based calculations of: a) the conductance of molecular junctions of phenyl-ethynylene wires covalently bonded to graphitic ribbons as a function of the bridge length, and b) the complex-band structure of poly-phenyl-ethynylene.Comment: version to appear in Chem Phys Lett; 8 pages, 4 figures; minor changes to the 06/08/03 submission (nomenclature and added concluding remark

Lattice Green's function approach to the solution of the spectrum of an array of quantum dots and its linear conductance

In this paper we derive general relations for the band-structure of an array of quantum dots and compute its transport properties when connected to two perfect leads. The exact lattice Green's functions for the perfect array and with an attached adatom are derived. The expressions for the linear conductance for the perfect array as well as for the array with a defect are presented. The calculations are illustrated for a dot made of three atoms. The results derived here are also the starting point to include the effect of electron-electron and electron-phonon interactions on the transport properties of quantum dot arrays. Different derivations of the exact lattice Green's functions are discussed