13-04-2013, 04:44 PM
Electronic Band Structure of Graphene
ABSTRACT
The band structure properties of graphene form the
basis of understanding the electronic spectra of carbonbased
allotropes of various geometries, such as graphite
or carbon nanotubes. We can use an analytical and numerical
descriptions of carbon’s valence electrons to better
understand the conduction and semiconductor properties
of these materials.
BAND STRUCTURE BACKGROUND
QUESTIONS
How many extended orbital basis func-
tions will you have for your material? Why?
A graphene sheet forms a two-dimensional hexagonal
crystal lattice with a primitive cell containing two atoms
(A and B); its lattice structure of graphene and its first
Brillouin zone is shown in Figure 1. The electron configuration
of free carbon atoms is 1s22s22p2. For the
two atoms in the basis, there are four valence orbitals,
yielding eight extended orbital basis functions for our
material. Because of its planar structure, atoms undergo
bonding with four hybridized sp2-wave functions
ABSTRACT
The band structure properties of graphene form the
basis of understanding the electronic spectra of carbonbased
allotropes of various geometries, such as graphite
or carbon nanotubes. We can use an analytical and numerical
descriptions of carbon’s valence electrons to better
understand the conduction and semiconductor properties
of these materials.
BAND STRUCTURE BACKGROUND
QUESTIONS
How many extended orbital basis func-
tions will you have for your material? Why?
A graphene sheet forms a two-dimensional hexagonal
crystal lattice with a primitive cell containing two atoms
(A and B); its lattice structure of graphene and its first
Brillouin zone is shown in Figure 1. The electron configuration
of free carbon atoms is 1s22s22p2. For the
two atoms in the basis, there are four valence orbitals,
yielding eight extended orbital basis functions for our
material. Because of its planar structure, atoms undergo
bonding with four hybridized sp2-wave functions