ABSTRACT
When an infinite graphene sheet is cut into nano-size graphene frag-
ments (nanographene) or semi-infinite graphene sheets, important
questions arise regarding the creation of graphene edges. This is
evident in early theoretical [1-6] and experimental works [7-13],
several of which predate the discovery of graphene in 2004 by many
years [14]. Depending on the direction of the line along which a
graphene sheet is cut, two distinct types of edge can be created, as
shown in Fig. 6.1: armchair and zigzag edges [13]. The electronic
structure of nanographene depends crucially on the geometrical
shape of the edges. In fact, according to theoretical [1-6] and
experimental studies [7-13], a nonbonding π electron state called
an edge state is created along zigzag edges, whereas no such state
appears in armchair edges. The presence of an edge state can be
H H H H
H
H H
H H
H
physically understood as a consequence of broken symmetry in
Dirac fermions at zigzag edges (see Chapters 2 and 4). The presence
or absence of edge states is relevant to the discussion in Chapter
5 regarding aromaticity in condensed polycyclic aromatic hydro-
carbon molecules [15-22], of which graphene can be considered
an indefinitely large version. In these molecules, nonbonding π
electron states are created with the same geometrical dependence
as in nanographene and graphene edges. Chemists describe the
presence of edge states as a result of the degradation of aromaticity.
