# Doping away From half filling

1. Feb 19, 2008

### JabberWalkie

Can someone tell me what Doping away from half Filling means? I see it everywhere. Although I can't find referance to it in Kittel or Mermin, although I might not be looking hard enough. I have and idea of what it is. Half filling refers to the doping where the Brillouin Zone is half holes and half half occupied states. So....doping away from half filling is going to be defined by, x=1/2+p, with x being the percentage of filled states in the Brillouin Zone and p being the Doping away from half filling.

I'm probably right about this, but im not sure, so its been bugging me. Any help would be apreciated, thanks.

2. Feb 20, 2008

### jpr0

You'd expect it to mean something like this... that the valence band is completely occupied while the conduction band is vacant.

[edit: you don't mean in the context of Landau Levels do you?]

Last edited: Feb 20, 2008
3. Feb 21, 2008

### JabberWalkie

4. Feb 21, 2008

### jpr0

Last edited by a moderator: Apr 23, 2017
5. Feb 21, 2008

### ZapperZ

Staff Emeritus
Well, I was hoping someone else would tackle this.... :)

The parent compound of the cuprate superconductor is a Mott insulator. By band structure calculation, the parent compound only have a half-filled state and should be a conductor. But it isn't. This is because the band structure calculation doesn't take into account the spin alignment at each hopping location. Because there is a long-range antiferromagnetic order in the compound. So even though each site is only occupied by one fermionic charge carrier (where there can be 2), the lower energy state for the system dictates that the hopping energy to go to another site is higher than to maintain the antiferromagnetic order. So that's why it is a half-filled state but still become an insulator.

Now, when you either ADD charges (i.e. add electrons) or when you remove charges (adding holes), then the long-range order is perturbed a bit, and there are locations for the charges to hop to (or for the holes to hop to). When you add these carriers, you are doping it away from half-filling, for obvious reasons. The whole system now either has extra electrons or extra holes. The material starts to become conducting, but not in the conventional sense (we call it "bad metals") because it exhibit many non-metallic behavior such as temperature dependence of the resistivity, etc.

So really, the doping away from half filling in cuprate superconductors is simply to get away from the insulating antiferromagnetic phase.

Zz.

6. Feb 21, 2008

### Gokul43201

Staff Emeritus
I would recommend that you start with the Hubbard model (e.g., in Solid State Physics, by Mihaly and Martin or any of the half dozen or so books devoted to the Hubbard Model).