Why doesn't BCS theory work for explaining cooper pairs in cuprate superconductors?
Because it can't predict the outcome of experiments. It's that simple.
People have tried modifying the BCS theory in various ways, but it simply doesn't work for the cuprates.
Note that this does not mean that ALL the results from the "classical" theories (BCS, Ginburg-Landau,London) are invalid, there are actually quite a few things that DO work which is why superconductivity in the cuprates is not considered to be a "separate" phenomenon from superconductivity in metals; they are cleary related but since we still do not understand WHY e.g. YBCO becomes superconducting we don't know how.
BCS says that if material has magnetic ion impurities (even very small amount) than this would destroy superconductive state (because of the interactions between Cooper pairs and unfinished atoms shell). Since the energy of coupling is much less than 1 eV pairs would be uncoupled by magnetism. YBCO ( Fe-based, Heavy-fermion systems are materials with magnetic ions and some of them even magnetically ordered).
Actually, the "coupling" in BCS is quite independent of the nature of the glue. So in principle, one could have magnetic coupling, such as spin fluctuation, as the glue in a BCS-type coupling. This is why this scenario has been one of those proposed for the mechanism in high-Tc superconductors. So while it is true that magnetic impurities can be detrimental to conventional superconductors, it doesn't automatically rule out BCS-type description just because the cuprates have an antiferromagnetic ground state.
Agree, but for now it was only one glue was found: phonon-glue. Spin fluctuation is a theory so far (with some possible scenarios). BSC perfectly explains low temperature SC with phonons but it definitely cannot be a phonons at high temperatures (because of interactions will be too strong for coupling) and it cannot be (at least only) phonons for the low-Tc (heavy-fermions, charge transfer salts) because of the magnetic order. So, theory which will explain unconventional SC would be not a BSC (at leas biggest part of it), otherwise unconventional SC would be explained for now with some assumptions to introduce magnetism here, but it doesn't.
Actually, for electron-doped cuprates, the phonon picture works pretty well. Certainly many of the ARPES spectra seem to be in agreement with the phonon coupling.
Please, do not tell that you really believe that in cuprates phohons can be responsible for the pairing.
Concerning pairing (as far as I remember) Cooper (before BSC) proposed that it can be some glue and after they three together create elegant theory which hold inside this phonon-caused coupling, isn't it?
I don't, but one cannot discount it yet. The half-breathing in-plane phonon mode has a strong-enough coupling to account for the high Tc.
It's not a matter of "belief". In fact, I've just finished refereeing an ARPES paper that showed an isotope effect on the strength of the "kink" in the ARPES spectrum even for a hole-doped cuprate. The breathing mode that I mentioned has a mode energy at 70 meV, right at the kink energy. Thus, one simply can't discount such things no matter what one "believes".
And if you had browsed the arXiv preprint yesterday, you would have noticed http://arxiv.org/abs/0808.0802" of the electron-doped compound that argued for phonons as being responsible for that observation. This is in addition to all the ARPES papers that have already been published out of Stanford and Z.X. Shen's group on the electron-doped cuprate. It is certainly premature to simply dismiss those (and several other scenarios including Anderson's RVB theory) at this point based on what we have.
Don't worry about the word "belief".
I've read that paper. Well, they said "most likely", means that they cannot prove (disprove) it. It sounds the same as "magnetic glue" or "spin density wave" stories, isn't it?. I am not very confident with these kind of materials, but thank you for this motivation. Unfortunately, (for this talk but not for me) I am on conference now, but later I'll look on it closer. Hear you soon.
I'm sure you know that there really isn't any "proof" for anything in physics. What they are arguing (and what most of the papers by Lanzara et al.) are arguing are that many of the signatures and variation with Tc are consistent with the phonon picture. Of course, the other camps with the magnetic channel picture would argue the same thing with their own set of experimental data. Until we get a lot more information, and experiments with better resolutions and sensitivity, this issue will remain unresolved.
Absolutely. Magnetic excitation DOS says that magnetic nature is responsible fo pairing. Who knows? Yesterday, I saw a few presentations and posters concernig exsaxtly the same questions. A few of them say "yes" to phonons (APRES) and other few say "yes" to magnetic nature. All this results are not published yet, but when it be published I'll give you links.
I've read some time ago that the Casimir effect between the cuprate planes could explain superconductivity in this case, basically because it lowers the energy of the system once superconductivity sets in.
Er.. no it doesn't, if you are referring to the still-unpublished work by Achim Kempf (from 2006, no less. I couldn't find any other citation to indicate that it has been published). He never described the mechanism for superconductivity, i.e. the origin of the pairing. All he tried was to formulate the "energetics" to match a few of the YBCO data, and this is AFTER superconductivity has sets in. YBCO is also not the "cleanest" system to do this because of the existence of the "chains" in the crystal structure along the c-axis. Besides, there's a major missing issue here that he never even tackled - the variation of Tc with doping, which has nothing to do with varying the distance between the CuO planes.
As far as I can tell, this idea hasn't been taken seriously.
What about this paper I read recently exploring the possibility of superconductivity from tunneling between copper oxide layers?
His english is a bit unpolished at parts, but it seems like an interesting idea. He claims to have calculated the pseudogap correctly for two materials so far. Any major arguments against it?
Phil Anderson, I think, had propose this "interlayer tunneling" mechanism way back in the early 90's. I believe this picture has been discredited with a number of experimental observation. I have only glanced through this and I don't see anything different based on what I can understand (it is not easy to follow).
We probably need to go easy on citing unpublished papers or else we'll never get to legitimate publications that do deserve the attention. Unlike high energy and string theory, it is still a very common practice that most of the main papers are published in peer-reviewed journals and not just done on arXiv. So we will stick to that practice.
May i correct your statement?
If we apply BCS theory to HTSC assuming phonon glue, then it is true, that BCS needs to have phonon frequencies which don't exist in cuprates. So the BCS must be incorrect for cuprates or must be modified.
In any of these cases we can imagine that Tc can depend of max phonon frequencies in another way. For example there can be resonance coupling, when gap is determined by high phonon resonance AMPLITUDE (remember the Froehlich one dimensional model of superconductor:
H. Froehlich, Proc. Roy. Soc. A223, 296-305 (1954) )
The gap in Froehlich 1D model is proportional to phonon AMPLITUDE, so there is no limitation to Tc (see eq. 2.28 and discussion after eq. 2.35), if the amplitude is sufficiently large.
The drawback(?) of Froelihch model is that it does not need Cooper pairing.
This is wrong. Read about the phonon half-breathing mode in the CuO plane:
S. Ishihara and N. Nagaosa, Phys. Rev. B. 69, 144520 (2004)
Z.X. Shen et al. Philosophical Magazine 82, 1349 (2002)
1 What is wrong? Can You disclose your argument straight here. What does "the phonon half-breathing mode in the CuO plane" can make wrong?
2. The main topic question is connected with BCS theory. By the way I don't found any "BCS" word in the second paper (Z. -X. Shen1,...) . Is "RVB picture in terms of the t-J models" the BCS model?
3. When anybody says about "strong" phonon coupling we have the right question him what does he mean? Is it phonon frequencies are very high or phonon amplitudes are very strong or both? BCS theory regarded maximum phonon frequencies as one of major factors for high Tc. And BCS didn't pay attention to possibility of phonon AMPLITUDE to be very strong and to consequences of such approach. But as i wrote the father of phonon picture of superconductivity Froehlich showed the example where phonon AMPLITUDE is very impotant.
4. I don't see anything "wrong" even after reading one of recommended papers and after being thought about what does it mean "wrong".
You claim that there are no phonon modes for the cuprates:
Those papers clearly show that there IS at least one phonon mode that can sustain the coupling strength called for with such high Tc. This has been used to justify the use of such phonon modes within the BCS theory
BTW, I think you have severely misunderstood BCS. While the BCS original paper did make use of phonons, BCS actually is quite independent of the "glue", which is why spin-fluctuation has also been used within the BCS scheme as one possible mechanism for the cuprates (D.J. Scalapino,Science 284, 1282 (1999)).
Yes, I see. I think you have severely misunderstood me. I have opposite opinion, that in majority of known HTSC cases phonon mechanizm is the dominant one. Even opposite to BCS conclusion, that Tc can't be more than the highest phonon FREQUENCY in the sample. I pointed out to the work of Froehlich as an example of another approach, where phonon AMPLITUDE is very impotant, and the gap can greately (10,100, 1000 times,...) exceed the MAXIMUM phonon frequency in the sample, and phonon wavelength (connected with phonon frequency) must be one half of electron wavelength at Fermi surface.
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