In the one-band model of strong coupling, the influence of substitutional impurity atoms on the energy spectrum and electrical conductance of graphene is studied. It is established that the ordering of substitutional impurity atoms on nodes of the crystal lattice causes the appearance of a gap in the energy spectrum of graphene with width η|δ| centered at the point yδ, where η is the parameter of ordering, δ is the difference of the scattering potentials of impurity atoms and carbon atoms, and y is the impurity concentration. The maximum value of the parameter of ordering is . For the complete ordering of impurity atoms, the energy gap width equals . If the Fermi level falls in the region of the mentioned gap, then the electrical conductance at the ordering of graphene, i.e., the metal–dielectric transition arises. If the Fermi level is located outside the gap, then the electrical conductance increases with the parameter of order η by the relation . At the concentration , as the ordering of impurity atoms η →1, the electrical conductance of graphene , i.e., the transition of graphene in the state of ideal electrical conductance arises.

MODERN ASPECTS OF SUPERCONDUCTIVITY Theory of Superconductivity PrefaceStudies of superconductivity theory are among the most fruitful and promising trends in the theoretical physics of condensed matter, since superconductivity remains one of the most interesting research areas in physics.The goal of this book is to give a representation of certain modern aspects of superconductivity. We discuss important aspects of the theory of superconductivity, such as the nature of high-T c superconductivity, two-gap superconductivity, room-temperature superconductivity, mesoscopic superconductivity, the pairing state and the mechanism of cuprate high-T c superconductivity.In Chap. 1, we consider the field-theoretical method of superconductivity and discuss the basic idea of superconductivity and the elaboration of the Ginzburg-Landau and Bardeen-Cooper-Schrieffer theories in the frame of many-particle quantum field theory.In Chap. 2, we consider the structures of high-T c superconductors, phase diagrams and the problem of pseudogaps, and analyze the mechanisms of superconductivity. We present general arguments regarding the pairing symmetry in cuprate superconductors and investigate their thermodynamical properties within the spin-fluctuation mechanism of superconductivity, by using the method of functional integrals.Chapter 3 concentrates on two-band and multiband superconductivity. We consider the physical properties of the superconductor MgB 2 and use our two-band model to explain the two coupled superconductor gaps of MgB 2 . To study the effect of the increasing T c in MgB 2 , we use the renormalization-group approach and phase diagrams. In the field of superconductivity we meet the problem-maximum, which consists in the creation of room-temperature superconductors. We consider this problem in our book and make some recommendations on the search for these superconductors. Chapter 4 deals with the problem of mesoscopic superconductivity. We consider the two-band superconductivity in ultrasmall grains, by extending the Richardson exact solution to two-band systems, and develop the theory of interactions between nanoscale ferromagnetic particles and superconductors. The properties of nanosize two-gap superconductors and the Kondo effect in superconducting ultrasmall grains are investigated as well.We also consider the ideas of quantum computing and quantum information in mesoscopic circuits. The theory of the Josephson effect is presented, and its applications to quantum computing are analyzed.This book deals with a wide scope of theoretical and experimental topics in superconductivity, and has been written for advanced students and researchers in that field. S. Kruchinin, H. Nagao and S. AonoKiev, Kanazawa, July 2009

We propose a simple model to study resonant tunneling through an organic molecule between to conducting leads, taking into account the vibrational modes of the molecule. We solve the model approximately analytically in the weak coupling limit and give explicit expressions for the thermopower and Seebeck coefficient. The behavior of these two quantities is studied as function of model parameters and temperature. For a certain regime of parameters a rather peculiar variation of the thermopower and Seebeck coefficient is observed.Although the model is very simple, we expect it to give some nontrivial insight into thermal transport properties through nan-devices. Furthermore, because we can provide an analytical solution, it may eventually serve as benchmark for more advanced analytical or computational methods. PACS numbers:

We employ Green’s function method for describing multiband models with magnetic impurities and apply the formalism to the problem of chromium impurities adsorbed onto a carbon nanotube. Density functional theory is used to determine the bandstructure, which is then fit to a tight-binding model to allow for the subsequent Green’s function description. Electron–electron interactions, electron–phonon coupling, and disorder scattering are all taken into account (perturbatively) with a theory that involves a cluster extension of the coherent potential approximation. We show how increasing the cluster size produces more accurate results and how the final calculations converge as a function of the cluster size. We examine the spin-polarized electrical current on the nanotube generated by the magnetic impurities adsorbed onto the nanotube surface. The spin polarization increases with both increasing concentration of chromium impurities and with increasing magnetic field. Its origin arises from the strong electron correlations generated by the Cr impurities.

Multi-band superconductivity is investigated by using two-particle Green's function techniques, and equations for coupled states are derived in the framework of a twoband model. These results suggest that superconductivity appears, even if electronelectron interaction is positive. We also present a cooperative mechanism for multi-band superconductivity.