Can someone explain peierls distortion/transition to me?

Click For Summary

Discussion Overview

The discussion revolves around the Peierls distortion and transition, particularly in the context of one-dimensional polymers like polyacetylene. Participants explore the implications of lattice spacing on electronic properties, including the formation of energy gaps and the behavior of conduction bands.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why a one-dimensional polymer with a half-filled conduction band experiences Peierls distortion and how changing the lattice spacing affects the energy gap.
  • Another participant explains that Peierls distortion involves alternating bond length changes, which open a band gap and lead to energetic stabilization, particularly in degenerate bands.
  • A participant expresses confusion and seeks a simple derivation of the concept, indicating difficulty in finding consistent resources.
  • Another participant suggests consulting Peierls' book "Quantum theory of solids" for further clarification on the topic.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and seek clarification, indicating that the discussion remains unresolved with multiple viewpoints and questions about the topic.

Contextual Notes

Some participants note the lack of accessible derivations and consistent resources, which may limit understanding of the Peierls distortion and its implications.

um0123
Messages
151
Reaction score
0
Peierls distortion states that for a 1 dimensional polymer (like polyacyteline) with lattice spacing a they should have a half-filled conduction band, why?

And how does changing the lattice space to 2a cause it to form an energy gap? In my mind it should be the same as the first case...
 
Physics news on Phys.org
The point is that in Peierls distortion, the bond length change, getting alternatinly longer and shorter. This opens a band gap and only the lower band will be filled, so you get energetic stabilization. This is especially easy to see for a degenerate band, e.g. think of largely spaced hydrogen atoms. If you pair them up into H2 molecules, you will get a full band of binding MO's and an empy band formed from anti-binding MO's.
 
im still fairly confused... is there a simple derivation somewhere i can follow? i tried looking one up but i can't seem to find anything consistent...
 
Did you check Peierls book "Quantum theory of solids" chapter 5.3?
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 20 ·
Replies
20
Views
4K
Replies
1
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 0 ·
Replies
0
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
1
Views
1K