7.7 For a square lattice in two dimensions: (a) Show that the kinetic energy of a free electron in a corner of the first Brillouin zone is a factor of two larger than that of an electron in the middle of the Brillouin zone edge. (b) Determine the corresponding factor for a primitive lattice in three dimensions. (c) Find out if the bands can overlap in a two-dimensional lattice by plotting the following dispersion relations for free electrons in a weak periodic potential. &(ky) for k, = 0 & (ky) for kx = πια ε(k) for kx = ky
7.7 For a square lattice in two dimensions: (a) Show that the kinetic energy of a free electron in a corner of the first Brillouin zone is a factor of two larger than that of an electron in the middle of the Brillouin zone edge. (b) Determine the corresponding factor for a primitive lattice in three dimensions. (c) Find out if the bands can overlap in a two-dimensional lattice by plotting the following dispersion relations for free electrons in a weak periodic potential. &(ky) for k, = 0 & (ky) for kx = πια ε(k) for kx = ky
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Please help answer all questions (a) (b) and (c).
This is a question on Solid State Physics
Transcribed Image Text:7.7 For a square lattice in two dimensions:
(a) Show that the kinetic energy of a free electron in a corner of the first Brillouin zone is
a factor of two larger than that of an electron in the middle of the Brillouin zone edge.
(b) Determine the corresponding factor for a primitive lattice in three dimensions.
(c) Find out if the bands can overlap in a two-dimensional lattice by plotting the following
dispersion relations for free electrons in a weak periodic potential.
&(ky) for k, = 0
& (ky) for kx = πια
ε(k) for kx = ky
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