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REFERENCE: https://borderlinerebel.wixsite.com/electrochemistrytext/quantum

PROBLEI'v-I 2. Band structure of graphene using tight binding [a] For a graphene layer, use semiempirical tight binding with Bloch sums of 303 orbitals on each carbon atom. Keeping only nearestneighbor hopping terms, compute the bandstructure in terms of the unperturbed energies 5,, of the p, orbitals and the hopping integrals V (pp, Tr]. Plot the band structure along selected highsynmietry lines and show the position of the Fermi energy. [b] \"Why do you obtain only two bands even though carbon has four valence electrons? [c] Approximate the bands near the K point {the corner of the hexagonal Brillouin zone). Show that the dispersion is linear near the K point and express the slope in terms of V [3319,11'}. If possible, nd Vl'dnp, it) from the literature and provide a nmnerical value for the slope of the dispersion. [Extra credit: 1iWhat fraction of the speed of light is the Fermi velocity?)