PHZ 6426 (Solid State I) Homework 6

Due Oct. 18

1. Solve Ashcroft and Mermin Problem 10.2.
2. Extension of Problem 10.2(c). Calculate, and produce an accurate plot of, the band structure of an fcc Bravais lattice along the following lines in the first Brillouin zone (see Fig. 10.5): OX, OL, OK, OW, LK, XW. Here O=(0,0,0), X=(2,0,0), L=(1,1,1), K=(3/2,3/2,0) and W=(2,1,0), all in units of pi/a. Indicate the precise energy of each level at the ends of each line. Assume that only nearest-neighbor gamma_ij are appreciable, and use the following data:
   • E_p = 0.8 eV
   • beta = 0.15 eV
   • gamma_0 = 0.025 eV
   • gamma_1 = 0.005 eV
   • gamma_2 = 0.010 eV