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Why is the valence band maximum for most semiconductors at the gamma point in the bandstructure view of dispersion relation

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The bulk of the question should define "gamma point" (k=0), and "bandstructure view" (you mean band theory) "of dispersion relation" (you mean the E(k) curve for an electron). A moving electron has more energy than an electron at rest, so it obviously takes less energy to move it to a higher band. Does this answer the question? Are you asking about the energy difference at the same k between different bands? Or are you asking about the energy to excite an electron at k to a higher band with a different k? What's the gap? You should specify this, I am not sure what the confusion is exactly. – Ron Maimon Sep 17 '12 at 9:10
Furthermore, I'm not even sure this is true. From memory (this is out of my comfort zone...): the $\Gamma$-point is only special if the crystal structure has inversion symmetry. – genneth Sep 17 '12 at 9:15
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@genneth: In any crystal with local hopping, the zero phase state is lowest energy, on general principles of positivity of wavefunctions (this is the stationary distribution for the stochastic process in imaginary time) and I just assumed that this is defined to be the gamma point in general. I think this would require breaking time-reversal symmetry to make the single-particle description have a lowest energy state elsewhere than on the constant wavefunction. I still don't know if the question is about this obvious thing, or about the gap at corresponding wavenumbers between different bands. – Ron Maimon Sep 17 '12 at 10:00
@ron maimon I am asking about the structure of the top most filled band, the valence band. In cases like graphene occurrence of band maximum is not at the Gamma point. – baalkikhaal Sep 18 '12 at 12:01
@genneth: I think the answer to the question lies in your hint that systems with inversion symmetry have band extrema at the gamma point. For example, graphene has no inversion symmetry. I will check it out and get back to you. – baalkikhaal Sep 18 '12 at 12:02

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