Nomenclature of high symmetry points in the bandstructure

In summary, the high symmetry points in the bandstructure are named according to certain rules. Points and lines within the Brillouin zone are represented by Greek letters, while those on the surface of the zone are denoted by Roman letters. The center of the Wigner-Seitz cell is always labeled as G. However, the same letters may represent different directions in different lattices. While this provides some understanding, it does not explain how the directions are named. A comprehensive list of these rules can be found in the International Tables of Crystallography, or in other resources like books or articles.
  • #1
abhi2005singh
63
0
Can anyone help me how the high symmetry points in the bandstructure are named. I know a few rules which are as listed below:
* Points (and lines) inside the Brillouin zone are denoted with Greek letters.
* Points on the surface of the Brillouin zone with Roman letters.
* The center of the Wigner-Seitz cell is always denoted by a G.
The same letters do not represent the same directions in different lattices.
This gives some idea but not how the various directions are actually named.
If the rules can be stated here, then good. If not please give some reference (book or article/paper) from which I can learn them and which can explain why they are named so.
Are they listed in the International tables of crystallography?
Thanks in advance.
 
Physics news on Phys.org

1. What is the purpose of nomenclature in bandstructure analysis?

Nomenclature in bandstructure analysis is used to label and identify the high symmetry points in the Brillouin zone. These points are important in understanding the electronic properties of a material and predicting its behavior.

2. What is a high symmetry point?

A high symmetry point is a point in the Brillouin zone where the symmetry of the crystal lattice is preserved. This means that the electronic properties at these points can be accurately described and used to understand the properties of the entire crystal.

3. How are high symmetry points named?

High symmetry points are typically named using the Miller index notation, which is a shorthand way of representing the directions and planes in a crystal lattice. The notation consists of three numbers, (h k l), which correspond to the directions along the three axes of the crystal lattice.

4. What are some common high symmetry points in a bandstructure?

Some common high symmetry points include the Gamma point (Γ), which is the center of the Brillouin zone, the X point, which lies on the edge of the Brillouin zone, and the M point, which lies on the diagonal of the Brillouin zone. Other common points include the K, L, and W points.

5. How can nomenclature of high symmetry points be useful in bandstructure calculations?

Nomenclature of high symmetry points is useful in bandstructure calculations because it allows for a simplified representation of the electronic properties of a crystal. This makes it easier to analyze and interpret the results of bandstructure calculations and can provide insight into the behavior of electrons in a material.

Similar threads

I Questions Regarding Primitive Unit Cell
    • Atomic and Condensed Matter
Replies
4
Views
2K
A Mapping High Symmetry Points from Primitive to Conventional Cell
    • Atomic and Condensed Matter
Replies
1
Views
930
Bismuth Telluride Bandstructure
    • Atomic and Condensed Matter
Replies
1
Views
3K
High symmetry points for a GaAs superlattice
    • Atomic and Condensed Matter
Replies
1
Views
4K
A Calculating asymptotic behavior of a correlation function
    • Atomic and Condensed Matter
Replies
2
Views
2K
Find the Rhombohedral Structure High-Symmetry Points of Bismuth
    • Atomic and Condensed Matter
Replies
1
Views
5K
Wigner-Seitz = Brillouin Zone?
    • Atomic and Condensed Matter
Replies
4
Views
9K
Where are the high symmetry points on a graphene band structure?
    • Atomic and Condensed Matter
Replies
3
Views
7K
High symmetry directions in a two-dimensional oblique crystal
    • Other Physics Topics
Replies
2
Views
1K
I Problems involving combinatorics of lattice with certain symmetries
    • General Math
Replies
2
Views
630

Hot Threads

Recent Insights

Back
Top