# Fermi Surface & Band Diagram Relationship?

## Main Question or Discussion Point

Can anyone help explain how one can apply information say from an energy band diagram of an element/compound to its respective fermi surface / "sphere"?

I understand there is a direct relationship, however, I can seem to physical interpret how one is able to say look at the energy band diagram and come out with a rough representation of what the fermi surface should look like...

Are there any resources that go in depth to this?

Any help is much appreciated.

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N8,

The highest occupied level (k_max) of a band-diagram corresponds to a point on the Fermi Surface. You could make a band diagram along any direction in the Brillouin Zone and the number of directions is infinite. So you could create a fermi surface if you determined k_max in all directions.

modey3

ZapperZ
Staff Emeritus
Can anyone help explain how one can apply information say from an energy band diagram of an element/compound to its respective fermi surface / "sphere"?

I understand there is a direct relationship, however, I can seem to physical interpret how one is able to say look at the energy band diagram and come out with a rough representation of what the fermi surface should look like...

Are there any resources that go in depth to this?

Any help is much appreciated.
Assuming that you truly mean the energy band diagram, then I'm not sure how you can. Such band diagram contains no k information, i.e. it has been integrated out.

To be able to get an idea of the actual Fermi surface, you need the full band structure, i.e. the E vs k diagram. For most real material, it can look like a "spaghetti" band structure, where various band lines are drawn along various crystallographic directions. For example, the "standard" band structure for Cu may look like this:

[PLAIN]http://www.personal.psu.edu/ams751/VASP-Cu/index_files/image010.jpg [Broken] [Broken]

[PLAIN]http://www.personal.psu.edu/ams751/VASP-Cu/index_files/image010.jpg [Broken] [Broken]

The Fermi surface will be formed by the occupied band that crosses the Fermi energy (E=0). So the k-values of the occupied band at the Fermi surface will form the Fermi surface.

Zz.

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