Undergrad Bands in strongly correlated materials

[dRic2]

The concepts of bands is a useful tool in describing electrons in solids, but as far as I understand it arises naturally only when the real interacting system of electrons can be mapped with a very good approximation to an independent-particles problem (a mean-field approximation). If I have strongly correlated material the correlation length is very big and standard mean-field methods begin to fail. In such a particular case do scientists keep talking about bands ?

Thanks
Ric

 

[davidbenari]

Yes they do keep talking about bands. Consider the system everybody is talking about nowadays: Twisted Bilayer Graphene. This is a material with a flat band structure and the cause of this is electronic correlation.

People that do theory consider correlation in the hamiltonian and then get a band structure. So yes, they do keep talking about bands.

 

[peterwang]

I can not agree with david. The cause of a flat band structure is not the electronic correlation. In fact, it is the atomic structure of the material that generates flat bands, if one uses the band theory to solve it. After getting the flat bands, we immediately know that the band theory is not reliable, because the "flatness" invites correlation effect into play.

 

[dRic2]

@peterwang I think I share your point of view but I was talking about mean fields approximation (like DFT), so a bit of correlation is built inside the effective potential that you use to solve the problem self-consistently. In this way you get a 1-particle equations and thus a band structure, but you are still "seeing" electron correlation (at least to some degree). The problem is when the correlation is too big (in space) and a mean field approach is not very helpful.