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

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 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

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

First-Principles Analysis of Molecular Conduction Using Quantum Chemistry Software

We present a rigorous and computationally efficient method to do a parameter-free analysis of molecular wires connected to contacts. The self-consistent field approach is coupled with Non-equilibrium Green's Function (NEGF) formalism to describe electronic transport under an applied bias. Standard quantum chemistry software is used to calculate the self-consistent field using density functional theory (DFT). Such close coupling to standard quantum chemistry software not only makes the procedure simple to implement but also makes the relation between the I-V characteristics and the chemistry of the molecule more obvious. We use our method to interpolate between two extreme examples of transport through a molecular wire connected to gold (111) contacts: band conduction in a metallic (gold) nanowire, and resonant conduction through broadened, quasidiscrete levels of a phenyl dithiol molecule. We obtain several quantities of interest like I-V characteristic, electron density and voltage drop along the molecule.Comment: Accepted for publication in J. Chem. Phys. (Special issue on molecular electronics, Ed. Mark Ratner

Landau-Zener transitions in a linear chain

We present an exact asymptotic solution for electron transition amplitudes in an infinite linear chain driven by an external homogeneous time-dependent electric field. This solution extends the Landau-Zener theory for the case of infinite number of states in discrete spectrum. In addition to transition amplitudes we calculate an effective diffusion constant.Comment: 3 figure

Coherent electron-phonon coupling and polaron-like transport in molecular wires

We present a technique to calculate the transport properties through one-dimensional models of molecular wires. The calculations include inelastic electron scattering due to electron-lattice interaction. The coupling between the electron and the lattice is crucial to determine the transport properties in one-dimensional systems subject to Peierls transition since it drives the transition itself. The electron-phonon coupling is treated as a quantum coherent process, in the sense that no random dephasing due to electron-phonon interactions is introduced in the scattering wave functions. We show that charge carrier injection, even in the tunneling regime, induces lattice distortions localized around the tunneling electron. The transport in the molecular wire is due to polaron-like propagation. We show typical examples of the lattice distortions induced by charge injection into the wire. In the tunneling regime, the electron transmission is strongly enhanced in comparison with the case of elastic scattering through the undistorted molecular wire. We also show that although lattice fluctuations modify the electron transmission through the wire, the modifications are qualitatively different from those obtained by the quantum electron-phonon inelastic scattering technique. Our results should hold in principle for other one-dimensional atomic-scale wires subject to Peierls transitions.Comment: 21 pages, 8 figures, accepted for publication in Phys. Rev. B (to appear march 2001