Nomenclature of high symmetry points in the bandstructure

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SUMMARY

The nomenclature of high symmetry points in bandstructure is defined by specific conventions: points and lines within the Brillouin zone are designated using Greek letters, while points on the surface are labeled with Roman letters. The center of the Wigner-Seitz cell is consistently represented by the letter 'G'. It is crucial to note that the same letters may denote different directions across various lattice structures. For further understanding, references such as the International Tables for Crystallography and the Wikipedia page on Brillouin zones provide comprehensive insights.

PREREQUISITES
  • Understanding of Brillouin zones in solid-state physics
  • Familiarity with crystallography terminology
  • Knowledge of lattice structures and symmetry operations
  • Basic grasp of band theory in condensed matter physics
NEXT STEPS
  • Research the International Tables for Crystallography for detailed nomenclature
  • Study the Brillouin zone and its critical points in solid-state physics
  • Explore the implications of symmetry in lattice structures
  • Learn about band structure calculations using software like Quantum ESPRESSO
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Physicists, materials scientists, and students studying solid-state physics who seek to understand the nomenclature and significance of high symmetry points in bandstructure.

abhi2005singh
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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.
 
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