Localized electronic states on graphite edge

Examining the band structure of graphite ribbons with a typical edge shapes of armchair or zigzag, we find that minute graphite in a nanometer scale shows a striking contrast in the π electronic states depending on the edge shape. A wide armchair ribbon can reproduces the electronic state of graphite, but a zigzag ribbon shows a pair of partly flat bands which gives a remarkable peak of density of states at the Fermi level. We derive the analytic solution of this peculiar Edge State, disclosing the puzzle of its emergence.