Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Why electrons in low lying levels of individual atoms stay localized in their own atoms in a crystal? Doesn't this contradict Bloch's theorem?

share|improve this question
add comment

1 Answer

They do not stay localized actually. It's only that their eigenstates (which are non-local) are very close in energy, and we can choose the basis of localized states and they would be close to eigenstates with high accuracy.

You can consider the tight-binding model, and take it to the limit of zero overlap of orbitals of neighboring atoms, and zero overlap integrals. That would be close to what low-level electrons in a crystal behave like.

share|improve this answer
    
So if there was only one electron in the crystal with lowest possible energy (1S orbital) it could be found on all nuclei with the same probability? –  richard May 9 '13 at 9:24
    
Yes (that would be the lowest state in the energy band, to which 1s energy level would expand to). But in that case the crystal would be unstable, because the average charge density would be positive then. To make a zero average charge density, you need to take as many electrons as protons in the nuclei. For the simpler model, consider 1 electron per 2 protons - an $\mathrm{H}_2^+$ hydrogen molecular ion. –  firtree May 9 '13 at 10:03
1  
and why these electrons couldn't conduct in Insulators if they are extended?(thanks) –  richard May 9 '13 at 10:07
    
Ha! That's a great question! That's because all the band is completely filled with electrons, and it consists of a complete set of wave vectors (quasimomenta). Thus, there are as many electrons moving from left to right, as moving from right to left. The total current of these electons is zero, and such bands take no part in conductivity, just the same as completely empty bands. Only partially filled bands can conduct anything, and those appear only in metals, semiconductors and such. See Fig. 1 in en.wikipedia.org/wiki/Electronic_band_structure –  firtree May 9 '13 at 11:30
    
then by applying an electric field you can destroy this balance and have current! no? –  richard May 9 '13 at 11:39
show 2 more comments

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.