Electron-electron interaction in nanographite ribbons

We study the pi electronic structure of graphite ribbons of a nanometer width by taking account of rise long-range electron-electron interaction. The primary features like energy dispersion and bond order distribution are essentially determined by the nearest-neighbor transfer alone, meaning their strong dependency on the connectivity relation in the pi electron network. The Coulomb interaction, on the other hand, is induced by the sites of longer distances as well, which means that the Coulomb repulsion reflects the site geometry in the atomic configuration. We focus on the geometry-dependent Coulomb interaction and discuss how it influences the electronic state near the Fermi level which is governed by the network topology. The Coulomb repulsion under the geometry of armchair ribbons works against the bond order distribution determined by the network topology. This may lead to a frustrated system especially for a quite narrow ribbon. The Coulomb interaction in zigzag ribbons tends to open a gap with/without bond alternation depending on the ribbon width. The gap, however; keeps the flatness of the center bands around k = pi and monotonically diminishes with increasing ribbon width, showing the anomalous character of the edge state.