Abstract: We present a Ginzburg-Landau theory for a two-band superconductor with emphasis on MgB2. We propose experiments which lead to identification of the possible scenarios: whether both sigma- and pi-bands superconduct or sigma-alone. According to the second scenario a microscopic theory of superconducting MgB2 is proposed based on the strongly interacting or-electrons and non-correlated pi-electrons of boron ions. The kinematic and Coulomb interactions of sigma-electrons provide the superconducting state with an anisotropic gap of s(*)-wave symmetry. The critical temperature T-c has a non-monotonic dependence on the distance r between the centers of gravity of sigma- and pi-bands. The position of MgB2 on a bell-shaped curve T-c (r) is identified in the overdoped region. The derived superconducting density of electronic states is in agreement with available experimental and theoretical data. It is argued that the effects of pressure are crucial to identify the microscopic origin of superconductivity in MgB2. Possibilities for increase of T, are discussed.

Abstract: Electron continement and its effect on the superconducting-to-normal phase transition driven by a magentic field and/or a current is studied in nanowires. Our investigation is based on a self-consistent numerical solution of the Bogoliubov-de Gennes equations. We find that in a parallel magneitc field and/or in the presence of a supercurrent the transition from the superconducting to the normal phase occurs as a cascade of discontinuous jumps in the superconducting order parameter for diameters D < 10 divided by 15 nm at T = 0. The critical magentic field exhibits quantum-size oscillations with pronounced resonant enhancements as a function of the wire radius.

Abstract: Using relativistic density-functional calculations, we examine the magneto-crystalline anisotropy and exchange properties of transition-metal atoms adsorbed on 2D-GaAs. We show that single Mn and Mo atom (Co and Os) strongly bind on 2D-GaAs, and induce local out-of-plane (in-plane) magnetic anisotropy. When a pair of TM atoms is adsorbed on 2D-GaAs in a close range from each other, magnetisation properties change (become tunable) with respect to concentrations and ordering of the adatoms. In all cases, we reveal presence of strong Dzyaloshinskii–Moriya interaction. These results indicate novel pathways towards two-dimensional chiral magnetic materials by design, tailored for desired applications in magneto-electronics.

Abstract: Few-electron systems confined in two-dimensional parabolic quantum dots at high magnetic fields are studied by the Hartree-Fock (HF) and exact diagoiialization methods. A generalized multicenter Gaussian basis is proposed in the HF method. A comparison of the HF and exact, results allows as to discuss the relevance of the symmetry of the charge density distribution for the accuracy of the HF method. It is shown that the energy estimates obtained with the broken-symmetry HF wave functions become exact in the infinite magnetic-field limit. In this limit the charge density of the broken-symmetry solution call be identified with the classical charge distribution.

Abstract: We investigate the adsorption process of small molecules on graphene through first-principles calculations and show the presence of two main charge transfer mechanisms. Which mechanism is the dominant one depends on the magnetic properties of the adsorbing molecules. We explain these mechanisms through the density of states of the system and the molecular orbitals of the adsorbates, and demonstrate the possible difficulties in calculating the charge transfer from first principles between a graphene sheet and a molecule. Our results are in good agreement with experiment.

Abstract: The electron and hole spectrum in single and bilayer graphene is derived from known one-dimensional models, and the relation between the spectrum and symmetry of the lattice is shown.

Abstract: We evaluate the transmission through magnetic barriers in graphene-based nanostructures. Several particular cases are considered: a magnetic step, single and double barriers, delta -function barriers as well as barrier structures with inhomogeneous magnetic field profiles but with average magnetic field equal to zero. The transmission exhibits a strong dependence on the direction of the incident wave vector. In general the resonant structure of the transmission is significantly more pronounced for (Dirac) electrons with linear spectrum compared to that for electrons with a parabolic one.