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HW5 - vectors are not orthogonal you must remember to...

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2D Graphene: a. With the p z basis and 2x2 matrix Hamiltonian used in class, calculate and plot the bandstructure along Γ -K-M- Γ . Also plot the expectation values of σ x and σ y for the conduction band wavefunction in the first BZ. b. Extend the Hamiltonian to include the s, p x and p y orbitals on both A and B sublattice sites, leading to an 8x8 matrix. Because the nearest-neighbor
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Unformatted text preview: vectors are not orthogonal, you must remember to trigonometrically decompose the overlap matrix elements into σ and π bonds! Recalculate the bandstructure. [One set of overlap parameters is V ss σ = ±4.80, V sp σ = 4.75, V pp σ = 4.39, and V pp π = ±2.56 eV (Phys. Rev. B 70 , 115407 (2004))]...
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