Question

Consider the free electron energy bands of an fcc crystal lattice in the empty lattice approximation in the reduced zone scheme in which all k’s are in the first Brillouin zone. Plot in the [111] direction the energies of all bands up to 6 times the lowest band energy at the zone boundary at = (2?/a)( 1/2 , 1/2 , 1/2 ). Let this be the unit of energy. This problem shows why band edges need not be necessarily at the zone center.

Hint: express as a multiple x of a (111) reciprocal lattice vector where 0 < x < 1. According to the empty lattice approximation, the energies of the bands are given by:

Answer 1