Can someone explain peierls distortion/transition to me?

In summary, Peierls distortion is a phenomenon in which the bond lengths in a 1-dimensional polymer change, resulting in a half-filled conduction band and an energy gap. Changing the lattice spacing to 2a causes this energy gap to form. This can be seen in the example of hydrogen atoms pairing up into H2 molecules, which results in a full band of binding molecular orbitals and an empty band of anti-binding molecular orbitals. A simple derivation of this concept can be found in Peierls' book "Quantum theory of solids" chapter 5.3.
  • #1
um0123
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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...
 
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  • #2
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.
 
  • #3
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...
 
  • #4
Did you check Peierls book "Quantum theory of solids" chapter 5.3?
 

1. What is Peierls distortion/transition?

Peierls distortion/transition is a phenomenon observed in one-dimensional crystalline materials where the lattice undergoes a distortion in its atomic arrangement at a critical temperature. This distortion leads to a change in the material's electronic and magnetic properties, resulting in a transition from a conducting state to an insulating state.

2. What causes Peierls distortion/transition?

The Peierls distortion/transition is caused by the coupling between the electrons and the lattice vibrations in one-dimensional materials. This coupling leads to an instability in the lattice structure, resulting in a distortion at the critical temperature.

3. How is Peierls distortion/transition studied?

Peierls distortion/transition is studied using various experimental techniques, such as X-ray diffraction, scanning tunneling microscopy, and Raman spectroscopy. These techniques allow scientists to observe the changes in the atomic and electronic structure of the material at the critical temperature.

4. What are the applications of Peierls distortion/transition?

Peierls distortion/transition has been observed in various materials, including organic polymers, inorganic compounds, and metals. This phenomenon has potential applications in the development of new electronic and magnetic devices, such as transistors, sensors, and memory storage devices.

5. Is Peierls distortion/transition reversible?

Yes, Peierls distortion/transition is a reversible phenomenon, meaning that the material can transition back to its original state when the temperature is changed. This reversibility is important for potential applications in electronic devices, as it allows for the control and manipulation of the material's properties.

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