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.
Resistivity is a measure of a material's ability to resist the flow of electrical current. It is directly related to both Hall conductance and longitudinal resistivity, as these are both properties that describe how easily electrons can move through a material.
Hall conductance refers to the flow of current perpendicular to an applied electric field, while longitudinal resistivity refers to the flow of current parallel to the electric field. This means that the two measurements are perpendicular to each other and are affected by different factors.
The resistivity of a material is affected by a variety of factors, including the type of material, its temperature, and any impurities or defects present. Additionally, the strength of the applied electric field can also impact resistivity.
Resistivity is typically measured using a device called a four-point probe, which applies a small electric current to the material and measures the voltage drop across it. This measurement can then be used to calculate the resistivity of the material.
Understanding these properties is important in many fields, such as materials science, electrical engineering, and physics. It allows us to design and optimize electronic devices, study the behavior of materials under different conditions, and develop new technologies for energy production and storage.