The contributed articles are presented in two volumes. The readers interested in ex- perimental studies of graphene are referred to the fi rst volume. The second volume contains theoretical contributions, divided into fi ve Sections. In Part I ab initio studies of the electronic structure of graphene in the presence of defects and impurities are described. In Part II the theory of graphene nano-fl akes and nano-ribbons is presented. | Part 2 Graphene Nano-dots and Nanoribbons 12 Physics of Triangular Graphene Motohiko Ezawa Department of Applied Physics The University of Tokyo Japan 1. Introduction Carbon forms many allotropic forms with different dimensionality three-dimensional diamond quasi-two-dimensional graphite 1 2 one-dimensional nanotubes 3-10 and zero-dimensional fullerenes 11 . These materials are well known to exhibit remarkable electronic properties depending on their geometry. There exists another form of carbon material graphene which is a monolayer graphite. Graphene can theoretically be considered the basic material for the other forms of carbon that can be obtained from it either by stacking graphite wrapping nanotubes or creation of topological defects fullerenes . Furthermore there are many derivatives in these graphene related materials. Their electrical properties such as carrier type particle or hole can be continuously controlled by the application of external gate voltage 12 . Graphite is made out of stacks of graphene layers that are weakly coupled by van der Waals forces. A pencil is a typical graphite. When we use it we are actually producing graphene stacks on a sheet of paper which may well contain individual graphene layers. Nevertheless it was only in 2004 when graphene was experimentally isolated 12 . They produced high quality large up to 100 ym in size graphene crystallites which immediately triggered enormous theoretical and experimental studies. Moreover the quality of the samples produced are so good that ballistic transport 12 and quantum Hall effects QHE have been observed 13 14 . For a recent review on graphene see ref. 15 . Edge states of graphene show a very remarkable feature. There are three type of edges zigzag edge armchair edge and Klein edge 16 . Graphene with a zigzag edge has the half-filled flat band at the zero-energy level and exhibits edge ferromagnetism 17 . These edge states can be observed by STM 18 19 . Among graphene derivatives .
