We present ab-initio time-dependent density-functional theory calculation results for low-energy collective electron excitations in MgB 2 . The existence of a long-lived collective excitation corresponding to coherent charge density fluctuations between the boron σ-and π-bands (σπ mode) is demonstrated. This mode has a sine-like oscillating dispersion for energies below 0.5 eV. At even lower energy we find another collective mode (σσ mode). We show the strong impact of local-field effects on dielectric functions in MgB2. These effects account for the long q-range behavior of the modes. We discuss the physics that these collective excitations bring to the energy region typical for lattice vibrations.PACS numbers: 74.25. Kc,71.45.Gm,73.43.Lp,74.70.Ad After several years of intense experimental and theoretical study of the origin of unusually high temperature superconductivity 1 in MgB 2 , nowadays there is a general belief that the superconductivity in MgB 2 is phonon-mediated with multiple gaps and an exceptional role played by E 2g phonon mode in strong coupling to electrons in the tubular-shaped σ bands at the Fermi level, E F . However, despite the tremendous progress achieved in understanding of superconductivity in MgB 2 , many of its fundamental properties related to phonons and electron-phonon (e − ph) coupling are still puzzling and remain under intense debate. Thus such important issues as, e.g., the reduced isotope effect, 2,3,4 the nature of the strong broad continuum in Raman spectra, the unusually broad linewidth of the E 2g phonon mode seen in Raman spectra, 5,6,7 the inconsistency between the results of Raman scattering and x-ray measurements, 8,9,10 and the role of non-adiabatic effects 8,11,12,13,14 have not yet found satisfactory explanations.As for the electronic part of the e−ph picture of superconductivity in MgB 2 , it has received substantially less attention than the phonon part. In particular, in all evaluations of the e−ph interaction the adiabatic approximation has been used, and even in ab initio calculations 15 of T c the dynamical Coulomb interaction has been considered in its static form. Here we present a detailed ab initio study of the low-energy dynamical electronic properties of MgB 2 . We demonstrate that the strongly anisotropic electronic structure of MgB 2 characterized by boron quasi two-dimensional σ and three-dimensional π bands 16,17 leads to remarkable low-energy dielectric response in this compound: collective modes with a peculiar sine-like oscillating dispersion appear in the 0-0.5 eV energy range. This brings interesting physics to the energy region which was thought to be entirely dominated by lattice vibrations.Our approach is based on time-dependent density functional theory 18 where the non-local dynamical densityresponse function, χ, determines an induced charge density, ρ, in the electronic system caused by an external potential, υ ext , according toχ is obtained from the integral equationis the response function of non-interacting electron system, υ(r − r ...

We report on the results of calculation of low-energy dielectric response and optical properties of MgB 2 . The calculations have been performed with full inclusion of the ab initio electron band structure making use of random-phase and time-dependent local-density approximations. The role of local-field and exchangecorrelation effects in MgB 2 dielectric function is thoroughly examined. Index of refraction, extinction coefficient, and normal-incidence reflectivity exhibiting strong anisotropy were calculated for electromagnetic waves polarized along the a ‫ء‬ and c ‫ء‬ axes by using the evaluated electron-density-response functions. Our results are in good agreement with recent x-ray and optical measurements performed on MgB 2 single crystals.

We investigate the localization of charged particles by the image potential of spherical shells, such as fullerene buckyballs. These spherical image states exist within surface potentials formed by the competition between the attractive image potential and the repulsive centripetal force arising from the angular motion. The image potential has a power law rather than a logarithmic behavior. This leads to fundamental differences in the nature of the effective potential for the two geometries. Our calculations have shown that the captured charge is more strongly localized closest to the surface for fullerenes than for cylindrical nanotube.

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