Electron scattering in the Brillouin zone boundary

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Discussion Overview

The discussion focuses on electron scattering at the Brillouin zone boundary, exploring its implications in real and reciprocal space, as well as its potential role in contributing to electrical resistance, similar to electron-phonon scattering at non-zero temperatures.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the nature of electron scattering at the Brillouin zone boundary, specifically its effects in real and reciprocal space.
  • Another participant suggests using the one-dimensional nearly free electron model to understand the phenomenon, noting that standing waves emerge near the Brillouin zone edge, leading to strong backscattering due to lattice periodicity.
  • A follow-up question is posed regarding whether electron scattering from the Brillouin zone boundary can contribute to resistance, akin to electron-phonon scattering, and requests an explanation for the answer.
  • One participant affirms that electron scattering could indeed contribute to resistance but acknowledges that the explanation is complex. They recommend standard undergraduate texts for further understanding.

Areas of Agreement / Disagreement

Participants express differing levels of familiarity with the topic, and while there is some agreement on the potential for electron scattering to contribute to resistance, the complexity of the explanation remains a point of contention. The discussion does not reach a consensus on the mechanisms involved.

Contextual Notes

Participants mention the need for a deeper understanding of the subject, indicating potential limitations in their current knowledge and the complexity of the topic. Specific assumptions about the models and their applicability are not fully explored.

Who May Find This Useful

This discussion may be of interest to students and researchers in solid state physics, particularly those exploring electron behavior in crystalline materials and the implications for electrical resistance.

Rzbs
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TL;DR
What exactly happen when an electron reach a Brillouin zone boundary?
I what to know what is electron scattering in Brillouin zone boundary?
What exactly happen for electron in Brillouin zone boundary; what happen for it in real space and what happen for it in reciprocal space?
And is electron scattering from a Brillouin zone boundary could be a source for resistance; I mean like electron-phonon scattering that cause resistance at not zero temperature?
Thanks for your help
 
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I recommend the one dimensional nearly free electron case as a vehicle to understanding. Near the edge of the Brillouin Zone, traveling waves give way to standing waves as the preferred solution...this can be described as "strong backscattering". because the periodicity of the wave is commensurate with the lattice . ( If you know optics this is similar to a multilayer notch interference filter )
 
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Thanks
So what about the second part of my quetion, "is electron scattering from a Brillouin zone boundary could be a source for resistance; I mean like electron-phonon scattering that cause resistance at not zero temperature?"
If yes; how? If not why?

And what is the best simple book for understanding this subject in details you suggest?

(And I must say I am not familiar with optics very much, unfortunately)
 
The answer to your question is yes it could but it becomes complicated. I recommend for solid state physics Ashcroft and Mermin or Kittel; there are many others that I am sure are adequate. These are standard undergraduate texts and I don't know any simpler texts.
 
Thanks
 

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