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I've been reading Kittel's book "Introduction to Solid State Physics" and I'm currently on the chapter of energy bands. I think I, at least partly, understand why energy bands are "created", because at k-values for bragg-reflection we have standing waves that distributes the electrons differently to the positive lattice ions.

But he is introducing the concept "band-overlapping" and I cannot wrap my head around this, does this mean that the low energy value for the next k-value (the next k-value "creating" the next brillouin zone" is overlapping the high energy value for the first k-value?

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  • $\begingroup$ Remember that $k$-space is 3D. There are often regions of overlap in energy between dispersion curves in different directions. $\endgroup$ – Pieter Apr 21 '18 at 7:11
  • $\begingroup$ But doesnt that mean that you would have overlapping in, lets say the fcc-brillouin zone, for the direction (110) and (011) always ? $\endgroup$ – John Skeet Apr 21 '18 at 7:17
  • $\begingroup$ In pure elements, metals is the ordinary case. There are just a few band insulators and those often have the diamond structure (fcc but with two atoms in the primitive cell). $\endgroup$ – Pieter Apr 21 '18 at 7:53
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It means that the energy range of different bands can overlap. Some states can have the same energy but for different k-values.

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