Reduced Zone Scheme of Free Electron Gas

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SUMMARY

The discussion centers on the reduced zone scheme of the free electron gas, specifically addressing the misconception about adding reciprocal lattice vectors to energy bands within the first Brillouin zone. It is established that the reduced zone scheme translates all energy bands into the first Brillouin zone, and adding a reciprocal lattice vector does not alter the position of a band within this zone. The conversation highlights the importance of understanding the periodic nature of energy branches in the extended zone scheme.

PREREQUISITES
  • Understanding of the Brillouin zone concept
  • Familiarity with reciprocal lattice vectors
  • Knowledge of energy band theory in solid-state physics
  • Basic principles of the free electron gas model
NEXT STEPS
  • Research the differences between the reduced zone scheme and the extended zone scheme
  • Study the implications of reciprocal lattice vectors on band structure
  • Explore the mathematical formulation of energy bands in solid-state physics
  • Examine practical applications of the free electron gas model in materials science
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Physicists, materials scientists, and students studying solid-state physics who seek to deepen their understanding of band structure and the behavior of electrons in crystalline materials.

exciton
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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
 
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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.
 
Edit: Yeah, you're right. There is only one possibility to move a branch in the 1. brillouin-zone.
Thanks.
 
Last edited:

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