Fermi Surface & Band Diagram Relationship?

In summary, there is a direct relationship between the energy band diagram and the Fermi surface of an element/compound. The highest occupied level on the band diagram corresponds to a point on the Fermi surface. To get a rough representation of the Fermi surface, the full band structure is needed, which can be obtained by plotting the energy vs. k diagram. Resources such as the "spaghetti" band structure for Cu can be used to visualize the Fermi surface.
  • #1
N8
6
0
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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  • #2
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
 
  • #3
N8 said:
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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1. What is a Fermi surface?

The Fermi surface is a representation of the boundary between filled and unfilled energy states in a solid material. It is a 3D surface in momentum space that shows the distribution of electrons at the Fermi level.

2. How is the Fermi surface related to the band diagram?

The band diagram shows the energy levels of electrons in a solid material. The Fermi surface is directly related to the band diagram because it represents the boundary between filled and unfilled energy states, which is determined by the Fermi level in the band diagram.

3. What information can be obtained from the Fermi surface and band diagram relationship?

The relationship between the Fermi surface and band diagram can provide information about the electronic properties of a material, such as its conductivity, thermal and magnetic properties, and its response to external stimuli like temperature and pressure.

4. How does the shape of the Fermi surface affect the properties of a material?

The shape of the Fermi surface directly affects the electronic properties of a material. For example, a small Fermi surface may result in higher conductivity due to the higher density of available energy states for electron movement, while a large Fermi surface may lead to lower conductivity.

5. How does the Fermi surface change with temperature and external stimuli?

The Fermi surface can change with temperature and external stimuli due to the redistribution of electrons in energy states. For example, an increase in temperature can lead to a larger Fermi surface as more energy states become available for electrons to occupy.

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