- #1

fluidistic

Gold Member

- 3,671

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## Main Question or Discussion Point

I would like to know every bit of information one can retrieve by looking at the Fermi surface of a material.

Here's what I think is correct thus far:

1) The fact that the material has a Fermi surface already tells us a lot. The material could be a metal or something that resembles a metal, but it's not an insulator (and not a semiconductor either?)

2) The more surface area, the more the charge carrier density and hence the higher the conductivity.

3) The local curvature of the Fermi surface tells us how the (quasi)electrons (or holes) would react when a small perturbation is applied, such as a thermal gradient, an electric field or a magnetic field. In other words, one gets the know the renormalized or effective mass of the charge carriers.

4) If the surface is actually blurred, so it's not a surface anymore, then the system is not exactly at absolute zero in temperature.

What I do not know but would like to know:

A) If we take for example lithium's FS. It is anisotropic, i.e. it isn't perfectly spherical and so the FS has a greater wavevector k in some direction compared to others. What exactly does this tell us regarding the resistivity of a Li cubic monocrystal? Does this mean that the resistivity is not uniform, i.e. it cannot be described by a single value but instead must be described by at least 2 values (so it's a tensor with at least 2 different entries)?

B) What does the absolute value of the wavevector on the FS tell us? I realize that a big wavector would mean a higher speed of charge carriers (the so-called Fermi speed), but what impact does this have regarding the material?

Here's what I think is correct thus far:

1) The fact that the material has a Fermi surface already tells us a lot. The material could be a metal or something that resembles a metal, but it's not an insulator (and not a semiconductor either?)

2) The more surface area, the more the charge carrier density and hence the higher the conductivity.

3) The local curvature of the Fermi surface tells us how the (quasi)electrons (or holes) would react when a small perturbation is applied, such as a thermal gradient, an electric field or a magnetic field. In other words, one gets the know the renormalized or effective mass of the charge carriers.

4) If the surface is actually blurred, so it's not a surface anymore, then the system is not exactly at absolute zero in temperature.

What I do not know but would like to know:

A) If we take for example lithium's FS. It is anisotropic, i.e. it isn't perfectly spherical and so the FS has a greater wavevector k in some direction compared to others. What exactly does this tell us regarding the resistivity of a Li cubic monocrystal? Does this mean that the resistivity is not uniform, i.e. it cannot be described by a single value but instead must be described by at least 2 values (so it's a tensor with at least 2 different entries)?

B) What does the absolute value of the wavevector on the FS tell us? I realize that a big wavector would mean a higher speed of charge carriers (the so-called Fermi speed), but what impact does this have regarding the material?