Question 1 Calculate the first few energy bands for free electrons in a two-dimensional square lattice, shown in the ba...
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...
2. Brillouin zone, rectangular lattice. A two-dimensional metal has one atom of valency one in a simple rectangular primitive cell a = 2 Â; b = 4 A. (a) Draw the first Brillouin zone. Give its dimensions, in cm. (b) Calculate the radius of te free electron Fermi sphere, in cm1. (c) Draw this sphere to scale on a drawing d the first Brillouin zone. Make another sketch to show the first few periods of the free electron band in...
Bottom pictures are 7.7 for context 7.4 Repeat the calculation of Section 7.7 for the empty lattice but for the foc case and the [111] direction. 7.7 The Empty Lattice and Simple Metals We again use our imaginary powers to control the strength of the potential. We assume a finite potential to define the lattice and then decrease it to an insignificantly low value so that the electrons become free. This is the empty lattice: it is a 'ghost' lattice,...