Generally phonon modes, or phonon self energies for coupling to electronic states do not contain momentum dependence. The direct excitation of a phonon from an electronic state or vice versa is not spatially dependent. This is what one would refer to as an electron-phonon interaction.

Bipolarons are different. If you bring two polarons close to each other, they can form a bound state, a bipolaron, which lowers their energy. One intuitively would presume that in the binding energy of the bipolaron there is some dependence on how close the polarons are spatially, or rather how much they overlap. I expect that there is no strict reason why NNN and further neighbour bipolarons should not form, they would simply be less dominant.

If the bipolarons form at very long distances, I believe you end up with overlapping bipolarons (effective bosons) which would condense into a bose-einstein condensate (or through a kosterlitz-thouless transition). There are theories of superconductivity coming from the binding of these jahn-teller polarons into finite range bipolarons, with claims that these are responsible for superconductivity in the cuprates. So while I do not off hand know the answer to your question regarding the range of these, I would suggest looking up jahn-teller (JT) models of superconductivity to see if someone has written what the coherence length of bipolaron formation is. I find it likely that it will be smaller than the electronic coherence length, maybe on the order of 20-40nm in the cuprates, but that is just a guess.

I'd like to learn more about the background which resulted in this

question. Why do I ask? There is a paper by S. Dal Conte et al.

Science 335, 1600 (2012) in which the normal state optical conductivity

of Bi2212 was analyzed. The authors come to the conclusion that a maximum of

20% of the total 'electronic' background is provided by the EP interaction.

This result agrees with an earlier paper by Schachinger and Carbotte,

Phys. Rev. B 81, 014519 (2010). They demonstrated that only about 10%

EP contribution to the total 'electronic' background is sufficient to explain

the oxygen isotope effect. observed in Bi2212. Thus, the EP interaction does not appear to be very important in high Tc superconductors.

I agree Ewald. It seems that there is quite a bit of literature looking for different short range quasiparticles (specifically bosons) which might give rise to superconductivity in the cuprates through a similar bosonic coupling as with phonons in the conventional case. I think that there is an experimental paper by LeTacon where they see what they're calling paramagnons (short ranged magnons). In the case of this bipolaron stuff, I believe it's just a different boson through which electrons might couple. But in that case, I'm not sure that they have been observed experimentally. Based on your comment, Ewald, anyone working on this must be under the impression that the electron-bipolaron coupling is strong over some very short length scale, in which case, bipolarons might be important while direct phonons are not? I don't see this being the case.

In 1993 we published a review paper about electron-phonon interaction in HTSC. I attch it to the reply. Maybe, it can be useful for you. You can download the English-language version free from

http://iopscience.iop.org/1063-7869/36/2/R02/pdf/1063-7869_36_2_R02.pdf

Now I am not sure that you can download the review In English free. If you need it, please ask me and I'll send you the English version.

thanks all for your opinions. Kindly send the review in english version to me.

Actually calculations on models on High tc materials such as Hubbard model or t-J model suggests that EP interaction may be relevant in different mechanism in these materials in addition to strong electron-electron interaction. Moreover experimental evidences support the above fact . In view of this fact we are trying to study the role of E interactions in high tc materials. So knowing this range of Ep interaction we can incorporate relevant terms in the Hamiltonian so that the model can resemble the real materials.

Dear Subhadip, Frankly speaking, I have no experience with Research Gate and have not found any possibility to attach a pdf-file to the message (most probably, do not know how to do it). Thus, please send your e-mail address to my e-mail [email protected] and I will send you the English version of our review. It was published 20 years ago at the beginning of the HTSC marathon but you can find there experimental data concerning the EPI range. If to speak about the HTSC mechanism, I have the same feeling (but only feeling!) as it is written in the answer by Dr. Schachinger, namely, that EPI is not the only and not the main mediator in the Cooper pairing in HTSCs. It can be that poaramagnons perform this role. In our tunneling measurements we have often oibserved signs of bosonic excitations different from phonons. .

The electron-phonon coupling constant \lambda is about \landa = 1 for cuprate superconductors but experimental determination is problematic. Since the coupling is strong the BCS theory fails and has not be modified appropriate for strong coupling (Migdal). One should also consider the role of magnetic fluctuations in superconductivity in cuprates. Tc scales with the resonance energy found in neutron scattering experiments.

Dear Subhadip, thank you for your information about the

background to your question. It is now clear to me what you are

planning to do. I think James in his first answer gave you a good idea

about the range of the EP interaction you were looking for.

By the way, our study on the oxygen isotope effect in Bi2212 was

based on an Eliashberg formulation of d-wave superconductivity

in optimally and overdoped cuprates. Foe underdoped cuprates

such a formulation doesn't exist yet to my knowledge.

Dear Subhadip,

I had two previous publications that it could help you to highlight the role of EP interaction in thermal conductionl /diffusion. you can read the abstracts and if you are intersted, I will send you the full text.

-Effect of cobalt doping on thermal conductivity of YBa2Cu3O7- delta superconductor.

BM Suleiman, L Börjesson, P Berastegui

Physical review. B, Condensed matter 04/1996; 53(9):5901-5906,

and

- The effects of cobalt substitution on the thermal diffusivity of YBa2Cu3O7−δ superconductor

B. M. Suleiman, L. Börjesson

[show abstract] [hide abstract]

Journal of Superconductivity 04/1997; 10(6):663-668.

Look a our revew

Sorry for tipos. Look, please, at our review.