The discussion revolves around the relationship between Hall conductance, longitudinal resistivity, and the density of states at the Fermi level. Participants explore theoretical aspects and seek clarification on how these quantities are related, particularly in the context of different dimensional systems.
There is no consensus among participants regarding the relationships discussed, and multiple competing views remain on the proportionality of Hall conductance and longitudinal resistivity to the density of states at the Fermi level.
Participants reference different dimensional contexts, suggesting that the relationships may vary depending on the system being considered. There are indications of missing assumptions and unresolved calculations related to these topics.
I need to think about this. I believe the derivative of the Hall resistivity w. r. to field is proportional to n(E_F).lion8172 said:I read somewhere that the Hall conductance is proportional to the derivative of the density of states at the Fermi level,
That looks right (for a 3d problem).and somewhere else that the longitudinal resistivity is proportional to the density of states at the Fermi level.