Doping away From half filling

  • Thread starter JabberWalkie
  • Start date
  • Tags
    Doping
In summary: In the simplest picture, the Hubbard model takes the bare band (which is a "metal") and adds on-site repulsion to prevent double-occupancy of a site. You can then think of it as a "molecule" of two on-site atoms or a "crystal" of two sites with one particle each. In the case of one band and half-filling, you have a half-filled band and the system is an insulator. Away from half-filling, the band is no longer half-filled and the system becomes a metal.In summary, doping away from half filling refers to the addition or removal of charges from a material with a half-filled band structure, resulting in a shift to a metallic state
  • #1
JabberWalkie
16
0
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 I am not sure, so its been bugging me. Any help would be apreciated, thanks.
 
Physics news on Phys.org
  • #2
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:
  • #4
Okay, looking at this paper from the same author

http://arxiv.org/PS_cache/cond-mat/pdf/0507/0507106v1.pdf

it's really not clear what x is, and I've never worked on anything related. ZapperZ would probably know...

[edit: this explains it http://physicsworld.com/cws/article/print/772/1/pw-13-02-08fig1 ]
 
Last edited by a moderator:
  • #5
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
JabberWalkie said:
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 I am not sure, so its been bugging me. Any help would be apreciated, thanks.
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).
 

1. What is "Doping away From half filling"?

"Doping away From half filling" refers to the process of introducing impurities, known as dopants, into a material to alter its electronic properties and shift its energy levels away from half filling, where the material has equal numbers of electrons and holes.

2. Why is doping away from half filling important in materials science?

Doping away from half filling allows for the manipulation of a material's electronic properties, such as conductivity and magnetism, which can be useful for various applications, including in electronics and energy storage.

3. How does doping away from half filling affect a material's band structure?

Doping introduces additional energy levels within a material's band structure, which can lead to the formation of new band gaps and alter the overall electronic properties of the material.

4. What are common dopants used in doping away from half filling?

Common dopants used in doping away from half filling include elements such as boron, phosphorus, and arsenic, which have different numbers of valence electrons compared to the host material and can thus alter its electronic properties.

5. Can doping away from half filling have negative effects on a material?

Yes, excessive doping can lead to the creation of defects and impurities within the material, which can negatively impact its electronic properties and structural integrity.

Similar threads

  • Atomic and Condensed Matter
Replies
2
Views
2K
  • Atomic and Condensed Matter
Replies
6
Views
3K
  • Atomic and Condensed Matter
Replies
4
Views
3K
  • Atomic and Condensed Matter
Replies
1
Views
7K
Replies
1
Views
2K
Replies
30
Views
5K
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
2
Views
4K
Replies
3
Views
911
  • Atomic and Condensed Matter
Replies
4
Views
2K
Back
Top