Reduced Zone Scheme of Free Electron Gas

  • Thread starter exciton
  • Start date
In summary, the conversation discusses the reduced zone scheme of the free electron gas and the possibility of adding a reciprocal lattice vector to move a particular energy branch in the first Brillouin zone. However, the extended zone scheme shows that the branches are already periodic and cannot be translated by a reciprocal lattice vector.
  • #1
exciton
14
0
Hi,

I was just wondering if there is any reason why the reduced zone scheme of the
free electron gas is looking like here (and in all other textbooks):

http://www.pha.jhu.edu/~jeffwass/2ndYrSem/slide19.html

I mean I could add any reciprocal lattice vector which moves
the particular energy branch in the 1. brillouin-zone.


thanks in advance
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
The reduced zone scheme is where all the bands have been translated into the first Brillouin zone. I don't really understand the question you are asking? You can't add a reciprocal lattice vector to a band to move it around in the zone, because the zone is the size of the reciprocal lattice vectors. Have a look at the extended zone scheme; the branches are periodic. if you add a reciprocal lattice vector to one of the bands, you translate it by exactly its period.
 
  • #3
Edit: Yeah, you're right. There is only one possibility to move a branch in the 1. brillouin-zone.
Thanks.
 
Last edited:

1. What is the Reduced Zone Scheme of Free Electron Gas?

The Reduced Zone Scheme of Free Electron Gas is a method used to simplify the calculation of energy levels in a solid material by considering only the electron states within a specific range of energy values, known as the reduced zone. This approach is commonly used in the study of electronic band structures in materials.

2. How does the Reduced Zone Scheme work?

The Reduced Zone Scheme works by taking the energy levels of free electrons in a solid material and mapping them onto a smaller range of energy values. This is achieved by folding the energy band diagram of the material into a reduced zone, which eliminates the need to consider all the higher energy levels outside of this zone. This simplification allows for easier analysis of the electronic band structure.

3. What are the advantages of using the Reduced Zone Scheme?

One of the main advantages of using the Reduced Zone Scheme is that it simplifies the calculation of energy levels in a solid material, making it easier to understand and analyze the electronic band structure. It also reduces the complexity of the equations used to describe the behavior of electrons in a solid, making it more accessible to researchers and students.

4. Are there any limitations to the Reduced Zone Scheme?

While the Reduced Zone Scheme is a useful tool for studying electronic band structures, it does have some limitations. It assumes a constant potential throughout the material, which may not be the case in some materials. It also does not take into account the effects of impurities or defects in the material, which can have a significant impact on the electronic properties.

5. How is the Reduced Zone Scheme used in practical applications?

The Reduced Zone Scheme is used in a variety of practical applications, such as in the development of new materials for electronic devices. By understanding the electronic band structure of a material, researchers can engineer its properties to optimize its performance in a specific application. It is also used in the study of semiconductors, where the reduced zone is often referred to as the Brillouin zone.

Similar threads

Dispersion relation for the free electron model
    • Atomic and Condensed Matter
Replies
1
Views
7K
A Properties of Degenerate Electron Gas
    • Atomic and Condensed Matter
Replies
5
Views
1K
A Are there phonons in a free electron gas?
    • Atomic and Condensed Matter
Replies
7
Views
2K
I Empty Lattice approximation/Nearly-free electron model
    • Atomic and Condensed Matter
Replies
2
Views
3K
Question about Bloch function in Reduced Zone Scheme
    • Atomic and Condensed Matter
Replies
1
Views
2K
Finding Distances to Brillouin Zone Borders from Origo
    • Atomic and Condensed Matter
Replies
4
Views
3K
A Thermal Properties of the Free Electron Gas: Fermi-Dirac Distribution
    • Atomic and Condensed Matter
Replies
1
Views
2K
I Free electron gas band structure?
    • Atomic and Condensed Matter
Replies
9
Views
4K
Confused by band theory in a weak potential
    • Atomic and Condensed Matter
Replies
3
Views
3K
A Calculating asymptotic behavior of a correlation function
    • Atomic and Condensed Matter
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top