Delocalized holes and trapped holes (polarons)

[Useful nucleus]

Are delocalized holes and trapped holes (polarons) mutually exclusive? Most of the density functional theory literature that I read and related to holes in metal oxides treats polarons and delocalized holes as mutually exclusive entities. The one with the lower formation energy is always assumed to be the one that is only present in the material (may be until certain temperature upon which the domination flips). Experimentalists also tend to explain conductivity measurements in this sense of mutual exclusiveness.
What I'm wondering, why isn't it possible to have two populations at the same time but at lower temperature the delocalized population dominates the conductivity and at higher temperatures the polarons do the the job?
Any thoughts or suggested references are appreciated?

 

[DrDu]

Are delocalized holes and trapped holes (polarons) mutually exclusive?

Are you familiar with the classical papers on the polaron problem by Pekar, Feynman and Lieb ( http://arxiv.org/pdf/cond-mat/9512112 )?

 

[Useful nucleus]

Indeed I'm not familiar with the work of those authors on Polarons. I'm surveying the recent literature (>2000) and gradually going to older (and as usual clearer) literature.
I had a look at the article you provided but still could not get hints about my question. Would you mind sharing your thoughts, please?

 

[DrDu]

I don't have too many thoughts on this subject. I only know that the correct description of the polarons and especially of the transition from light to heavy polarons was quite a difficult problem. There were good Ansätze in both regions, but I think Feynman was the first to give an approximation which was reliable in both regions.

Clearly, it involves non-adiabatic effects, i.e. the coupling of electronic and nuclear motion, so I don't know whether you can describe this very well using DFT.

Whether a polaron is heavy or light depends on the strength of the electron phonon coupling which depends on the material. Therefore I would expect in a given material either heavy or light polarons and not both at the same time.

 

[Useful nucleus]

Thank you, DrDu!
There are DFT attempts to do determine whether a hoping pathway for the small polaron is adiabatic or non-adiabatic. And in both cases one resorts to Marcus theory of electron transfer (developed originally for ions in aqueous solutions) to calculate the hoping rate. A nice example for this is the following paper:

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.75.195212

 

[DrDu]

Thank you! Yes, this makes sense. I don't have access to the article at the moment. Do you know how they determine the electronic coupling from DFT?

Edit: Ah, I just found another paper by the authors. They use some semi-empirical formula in combination with UHF calculations on clusters.
I also don't find this DFT+U method very convincing. I would give some DFT with exact exchange a try.