PHZ 6426 (Solid State I) Homework 4

Part A (due Sep. 20)

1. Construct the "empty lattice" band structure of an fcc Bravais lattice along the (111) reciprocal lattice direction. Draw the energy bands along this direction within the reduced zone scheme. Show all levels up to an energy six times that of the lowest band at the zone boundary. Indicate the precise energy of each level at the zone center and zone boundary.
2. Ashcroft and Mermin Problem 9.3.

Part B (due Oct. 6)

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 = 0.1 eV
   • gamma_0 = 0.02 eV
   • gamma_1 = 0.01 eV
   • gamma_2 = 0.015 eV