Understanding Band Theory: The Difference Between Conductors and Insulators

[Pdawgg]

My question is as follows: if you place an insulator into an applied field, the only thing that will happen is that the potential energy of each band will shift, according to the potential that it is in. Why is this exact same thing not what takes place in conductors? Why do the electrons at the fermi level gain kinetic energy instead of potential energy, like the electrons in the other bands?

This is a simple question and I know it will have an embarrassingly simple answer, but I am tired and cannot explain it or figure it out right now. Thoughts?

 

[Pdawgg]

Since there's no way to delete: the answer is obvious. Of course the electrons will gain kinetic energy: they are trying to minimize their potential energy...