Why does half-filling in a lattice result in a zero chemical potential?

[Niles]

Hi

1) I have read in an article that the atoms in a lattice are at "half-filling". As I understand, this means that the chemical potential is zero. Why does "half-filling" mean since it equals that the chemical potential is zero?

2) Let's say that I place an impurity with potential U₀ in my lattice. Does it make a difference whether U₀ is positive or negative? What is the usual case?

Best regards and happy Easter,
Niles.

 

[kanato]

1) Half filling means every site in the lattice has a single particle. Since each site can hold two particles, you are at helf filliing. The chemical potential being zero is a consequence of having a symmetric band structure and an on site energy of zero.

2) Yes it matters whether U0 is positive or negative. I think there is no usual case, it depends on what kind of model you want to study.

 

[Niles]

Thanks. Regarding #2, if I set U0>0, then it "costs" more energy to be there, right?

 

[kanato]

Right