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Tight-Binding Band Structure of Graphene: Graphene is a honeycomb lattice (Eq. (1.5)) with lattice spacing a = 2.46 Å (Table 2.1). The electronic band structure of graphene can be computed to reasonable approximation from s and p orbitals. The bands break into two groups. There is a first set of bands that come from the interactions of the s orbital and the px and py orbital, assuming graphene sits in the x-y plane. These are the o bands, which require solution of a 6 × 6 matrix problem, described by Saito et al. (1998). A second set of bands comes from the p₂ orbitals, called the bands. These can computed completely independently from the o bands because all integrals of the form ſ dřaª (7)aª¹(7) or ſ dřaª (7)aª (7) vanish by symmetry. Thus for the π bands there is only one orbital at to consider, cylindrically symmetrical in the x - y plane, and with symmetry like z in the 2 direction. Because the honeycomb lattice is built from two basis vectors, the matrix in Eq. (8.32) is 2 x 2.

Tight-Binding Band Structure of Graphene: Graphene is a honeycomb lattice (Eq. (1.5)) with lattice spacing a = 2.46 Å (Table 2.1). The electronic band structure of graphene can be computed to reasonable approximation from s and p orbitals. The bands break into two groups. There is a first set of bands that come from the interactions of the s orbital and the px and py orbital, assuming graphene sits in the x-y plane. These are the o bands, which require solution of a 6 × 6 matrix problem, described by Saito et al. (1998). A second set of bands comes from the p₂ orbitals, called the bands. These can computed completely independently from the o bands because all integrals of the form ſ dřaª (7)aª¹(7) or ſ dřaª (7)aª (7) vanish by symmetry. Thus for the π bands there is only one orbital at to consider, cylindrically symmetrical in the x - y plane, and with symmetry like z in the 2 direction. Because the honeycomb lattice is built from two basis vectors, the matrix in Eq. (8.32) is 2 x 2.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Tight-Binding Band Structure of Graphene: Graphene is a honeycomb lattice (Eq. (1.5)) with lattice spacing a = 2.46 Å (Table 2.1). The electronic band structure of graphene can be computed to reasonable approximation from s and p orbitals. The bands break into two groups. There is a first set of bands that come from the interactions of the s orbital and the px and py orbital, assuming graphene sits in the x-y plane. These are the o bands, which require solution of a 6 × 6 matrix problem, described by Saito et al. (1998). A second set of bands comes from the p₂ orbitals, called the bands. These can computed completely independently from the o bands because all integrals of the form ƒ dra³ (7)aª¹(7) or ſ dřaª (7)aª (7) vanish by symmetry. Thus for the π bands there is only one orbital at to consider, cylindrically symmetrical in the x - y plane, and with symmetry like z in the 2 direction. Because the honeycomb lattice is built from two basis vectors, the matrix in Eq. (8.32) is 2 x 2.
Transcribed Image Text:Tight-Binding Band Structure of Graphene: Graphene is a honeycomb lattice (Eq. (1.5)) with lattice spacing a = 2.46 Å (Table 2.1). The electronic band structure of graphene can be computed to reasonable approximation from s and p orbitals. The bands break into two groups. There is a first set of bands that come from the interactions of the s orbital and the px and py orbital, assuming graphene sits in the x-y plane. These are the o bands, which require solution of a 6 × 6 matrix problem, described by Saito et al. (1998). A second set of bands comes from the p₂ orbitals, called the bands. These can computed completely independently from the o bands because all integrals of the form ƒ dra³ (7)aª¹(7) or ſ dřaª (7)aª (7) vanish by symmetry. Thus for the π bands there is only one orbital at to consider, cylindrically symmetrical in the x - y plane, and with symmetry like z in the 2 direction. Because the honeycomb lattice is built from two basis vectors, the matrix in Eq. (8.32) is 2 x 2.
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