抄録
Nanoelectronics based on graphene has become a fast growing field with a number of technical applications. In these circumstances, we perform numerical study of the existence of flat bands (FB) in graphene ribbons, in consideration of zigzag and Klein's bonds with periodic distribution for all cases in which N ≦10, where N denotes the period of the edge pattern. As a result, the electronic state at Fermi energy of graphene ribbons can be categorized into four types, depending on the period and the density of the Klein's bonds (NK), R≡NK/2N; These are type (i) where FB disappears, type (ii) ribbons that have only FB, type (iii) ribbons possessing only partially flat band (PFB), and type (iv) containing both FB and PFB. When Nincreases in type (iv), double degeneracy of PFB is maintained, while degeneracy of FB increases. Systems of N = 3n are classified into categories types (i) and (ii), while systems of N≠3n belong to types (iii) and (iv). We would like to emphasize that above properties for appearances and disappearances of PFB and FB are dominated only by numbers of Klein's bonds in corresponding unit cells for N periods. Namely, those are independent of positions of Klein's bonds. The relationship between those properties in ribbons and the role of Dirac K-points originating from graphene is discussed.
