What is an electron/hole pocket and what is the significance? I'm trying to get my head around this. I've read what Ashcroft and Mermin have to say on the subject, but it's a little convoluted. They talk about the 1st, 2nd, 3rd, etc Brillouin Zones (BZ), and then show that, as you increase the radius of the free electron Fermi sphere (FS), parts of its surface will lie within certain BZ's.
From there, you do this kind of strange process of taking the parts of the FS that lie within the nth BZ, and translate it with reciprocal vectors so they're within the 1st BZ. It seems like (in the example they use of a FCC metal) the "electron pockets" come from the 4th BZ being translated into the first.
I understand what they're doing, but I don't really see why. I also don't really see the significance of the pockets, but I keep seeing them mentioned in papers. I have a suspicion -- do they (reduced) BZ's (i.e., after you translate the appropriate part of the nth BZ into the 1st BZ) represent different bands (n = 1,2,etc), and the electron/hole pockets represent the highest band?
Any other elucidation would be greatly welcomed as well.