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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.

We predict the existence of low-frequency nonlocal plasmons at the vacuum-surface interface of a superlattice of N graphene layers interacting with conducting substrate. We derive a dispersion function that incorporates the polarization function of both the graphene monolayers and the semi-infinite electron liquid at whose surface the electrons scatter specularly. We find a surface plasmon-polariton that is not damped by particle-hole excitations or the bulk modes and which separates below the continuum mini-band of bulk plasmon modes. The surface plasmon frequency of the hybrid structure always lies below , the surface plasmon frequency of the conducting substrate. The intensity of this mode depends on the distance of the graphene layers from the conductor’s surface, the energy band gap between valence and conduction bands of graphene monolayer and, most importantly, on the number of two-dimensional layers. For a sufficiently large number of layers the hybrid structure has no surface plasmon. The existence of plasmons with different dispersion relations indicates that quasiparticles with different group velocity may coexist for various ranges of wavelengths determined by the number of layers in the superlattice.

This paper presents an analytical and numerical investigation of the energy spectrum of two-dimensional Bloch electrons subject to a periodic potential of square and hexagonal symmetry and a perpendicular sine-modulated magnetic field, applying the tight-binding model. The energy spectrum is found using an effective Hamiltonian obtained by employing the Peierls substitution in the ground-state energy band function. The resulting Schrödinger equation is solved by applying a matrix method. The energy spectrum found exhibits recursive properties similar to those discussed by Hofstadter for the case of a uniform perpendicular magnetic field. It is the objective of this paper to show that this technique can be extended successfully in the presence of a modulated magnetic field of arbitrary strength. We successfully demonstrate a Hofstadter-type spectrum in the presence of both a uniform and a modulated magnetic field.