Unformatted text preview: Problem set 7 This problem deals with the effects of orbital symmetry and size in a tight-binding band structure. The idea is to model the band structure of a transition metal with valence s and d bands. Recall that these bands may come from orbitals of different principle quantum numbers, and therefore have of very different atomic radii. For example, Cu has 4s and much smaller 3d orbitals in the valence band. Thus, take two valence orbitals on each lattice site in a two-dimensional square lattice (of lattice constant a = 1). One of these orbitals should be a d-orbital, and one an s-orbital. For simplicity, approximate ψ d = ψ d e- r/a d ( x 2- y 2 ) ψ s = ψ s e- r/a s (1) where r = p x 2 + y 2 and let a s = 1 . 5 and a d = 0 . 9 in units of a . Calculate ψ d and ψ s to normalize the wave functions, then taking the perturbation v as a sum of screened coulomb potentials ( v a/ ( r + 0 . 001) Exp [- r/a ]–the small number is added to the denominator to cut off the divergence) on the four nearest neighbors, calculate the overlap orbitals called...
View Full Document
This note was uploaded on 01/10/2012 for the course PHYSICS 707 taught by Professor Electrodynamics during the Fall '11 term at LSU.
- Fall '11