ABSTRACT
In this chapter we consider a tight-binding model which formerly
was suggested for graphite.We implement thismodel to describe the
stack with a finite number of graphene layers and also to explore the
quantized states in the ribbons of bilayer and single-layer graphene.
Electron properties of the simplest bilayer consisting of two
monoatomic graphene sheets which are stacked one on top of
another (see Fig. 3.1a) indicate new anomalies not visible in mono-
layers (McCann et al. 2006). Thus, the graphene bilayer is modeled
as two coupled hexagonal lattices consisting of four nonequivalent
sites A, B and A˜, B˜ in the bottom and top layers, respectively (see
Fig. 3.1b). One writes the tight-binding Hamiltonian for the bilayer
graphene as
