BCS theory is based on the idea that virtual phonons couple the electrons into Cooper pairs. Not even the pairing mechanism is clear in high T_C superconductors. The physics can be very different.
One main objection to the BCS theory as applied to the high-Tc superconductors is that this theory is founded on the notion of the Landau quasiparticles, which in these superconductors, especially in the underdoped region, are not well-defined. In other words, the starting point of the BCS theory is a mean-field theory for the electronic degrees of freedom; coupling these mean-field electrons to bosonic excitations (such as phonons, as pointed out by Christian Binek hereabove, but not exclusively [1]), one can arrive at a superconducting state, depending on the physical conditions (such as temperature). In high-Tc superconductors this hierarchical separation of the degrees of freedom does not apply.
[1] Consult, for instance, D Pines, Understanding High Temperature Superconductors: Progress and Prospects, Physica C 282-287, 273 (1997), and the references herein.
https://doi.org/10.1016/S0921-4534(97)00253-0
Dear Christian,
BCS theory of superconductivity needs to exchange phonons between two electrons for creating Cooper pairs quasiparticles close to the Fermi level. As they are bosons thus they are not limited by the Pauli's exclusion principle and thus they try to share the same state, The main problem is that the phonons put a limit of the temperature (Debye temperature) and such a limit was calculated in the past to be around 30K. That is to say, upper 30K couldn´t exists superconductivity without having a crstalline lattice broken. This is in short the incompatibility between BCS and the high Tc superconductors which present a much higher critical temperature.
For solving such difficulty there are many models, but one is quite well developed uses magnons intead of phonons as exchange particles between the electrons (having an antiferromagnetic background in their insulation phase) allowing bound pairs in states with d-symmetry. This is called d-superconductivity, there is also p-superconductivity and s-superconductivity (which coincides with the usual BCS).
A good reference for understanding the difficulties of this issue is:
P.W. Anderson, Science 235, 1196 (1987)
Dear Daniel, regarding the lattice instability to which you refer (generally referred to as one of Anderson's theorems), you may wish to consult my relevant remarks in the footnote of p. 947 of the attached paper (Phil. Mag. 84, 909-955 (2004)).
Article On the break in the single-particle energy dispersions and t...
Dear Behnam,
Thank you very much for your paper. It seems interesting (is very long and I didn't yet read it) but the not that you say is a little far of what I tried to present as the fail of BCS in the new superconductors. It was predicted in the past that the limit of the critical temperature for having superconductor phase was arond the 30K. Thus BCS cannot be compatible (ir only phonons are used as exchange particle) with Tc-superconductivity.
By the way Migdal's theorem is well known that it doesn't work in heavy fermions and in the Tc-superconductivity needs to be reformulated using the fact that these materials have a very small fermi energy. In fact the Born-Oppenheimer approximation which it supstitutes is difficult to imagine for me.
Dear Daniel, you are welcome. I should perhaps point out that in my previous comment on this page I referred to my remarks in a footnote, and not the entire paper; therefore the length of the paper is not very relevant (except that the footnote is longer than a typical footnote in a short paper). Incidentally, in the same footnote I also emphasise the way the Migdal theorem under discussion is tied to a particular model, characterised by a specific electronic energy dispersion.
Dear Benham,
Thank you, it seems that the paper could be interesting over all if one would be interested in seen the conditions of the quasiparticle existance within the Landau background. But I repeat that I have only tried to answer directly the question made by Muhammad and I wrote the name of Christian because I only added something more to his argument of the photon (no virtual photon because in fact this is not a real interaction between electrons, which is made obviously by the photons).
sorry I have to write phonon instead of photon
" his argument of the phonon (no virtual phonon because in fact this is not a real interaction between electrons, which is made obviously by the photons)".
Dear Daniel, I merely intended to point out that the old argument of 30K, lattice instability, and all that, is really not generally applicable. It is model dependent.
Dear Behnam,
I don't understand your argument properly, sorry, how do you explain that the existence of phonons at 90K coupling to the electrons close to Fermi level ? For me this is the real difficulty of BCS, what do you think about? It is true that the phonos are not the only source of the critical temperature and the electrons give also a considerable part.
Dear Daniel, I did not make any claim of the kind you are suggesting, and in fact, as you can verify, the main observation of my relevant paper is that phonons cannot be directly responsible for the 'kink'. You are posing the six-million dollar question, but let me suffice to mention that there are people (mostly from the Russian school) who are quite happy with the electron-phonon scenario.
Dear Behnam,
Thank you, now I understand you and we are in agreement. This is a quite difficult question that I don't believe that the phonons are able to solve as exchange particles alone. It was so beautiful the BCS theory that we are still within its conceptual frame.
You are welcome Daniel. The theoretical and conceptual framework of the BCS remain, the difficulty is that the hierarchical structure common to the conventional superconductors (in which Landau quasi-particles are well-defined and one naturally couples them to some bosonic degrees of freedom) is missing, or at least shaky. We are used to free-field theories perturbed by some weak perturbations, but over the years in particular particle theorists have come up with some very interesting and novel techniques for dealing with strongly-coupled problems. It is therefore only a question of when, not whether, some or a group of people will have solved the problems associated with the cuprate superconductors. Be it as it may, last year, PW Anderson published a very interesting 'Last Words' on the cuprates, here:
https://arxiv.org/abs/1612.03919
https://arxiv.org/abs/1612.03919
Dear Benham,
Thank you but I knew it: too many concepts but very few results.
In superconductivity the first difficulty is about the notion of free conduction electrons.
In the early part of the twenty century the electrons of the conduction band were thoughtf as free. This is quite evident when current flow is established. However, it is also important to be able to describe conduction electrons in the absence of current flow. In a solid there are correlations between the positions of different conduction electrons, which minimize their repulsive interactions. A simple solution to describe these correlations is to suppose that each conduction electron, at low temperature and in the absence of current flow, belongs to one atom. This implies that there is a gap, which localizes conduction electrons when there is no external interaction, which may free them. See “Conductivity and statistics, an alternative view”.
This remark has lead me to propose a more complete statistical distribution of the thermal energy see “Perturbations and Statistical Distribution of the Thermal Energy” where I discuuss the limit of the validity of the Boltzmann relation.
Dear Muhammad
normally, high temperature superconductor does not obey to BCS theory because the high temperature greater than 30 K is suitable to destroy the cooper pairs, which are responsible on the conductivity mechanism of superconductor compound.
Dear All, In the work “Conductivity, Superconductivity and Defects” It is underlined that the defects, in high-Tc superconductors, are sources of conduction electrons. Without defect the compound would be an insulator with conduction electrons strongly localized each one on its atom. As a result the defects allow to better apprehending the existence of a gap for the conduction electrons in the normal state. This interpretation is built with a mechanism of superconductivity supported by the experiments of photoinduced conductivity and by the flux quantum h/2e. The model allows to explain the existence of oxygen 2p holes in n type superconductors. It also shows why the law of the thermal variations of the Ba NQR frequency does not vary with the insulator or metallic character of the compound.
As a result it is not surprising that BCS theory has difficulty to clarify the HTCSC, Yours Xavier
In conductivity and superconductivity there is a very surprising approach: the use of quantum property to determine the statistical distribution of the thermal energy. Indeed there is no clear understanding of origin of the quantum properties and it is supposed additional quantum properties in statistic. For example the electron is supposed undiscernible, this is an error: as soon as we consider the volume of the particle it possible to fully determine the statistical distribution of the thermal energy and we do not need the use of Pauli Exclusion Principle, see for example “The Most Probable Distribution of the Thermal Energy”. In place to suspect a wrong hypothesis in statistic the study of the superconductivity had led to the BCS theory adding the hypothesis of the pairing. It was the wrong way.
But what is important to realize is how we can easily work out of the logic and to be unable to question our previous work. I think we like the Magic as the question “111 years of Magic are enough: Let us return to Science now” underline this propensity considering relativity. The researcher is perhaps a child during a long time but we must become an adult to progress in our work. Be careful to avoid to regard the Fermi, the Einstein, the Dirac and so on as Gods, they were men and we have to improve their work, all man is able to mistake. The difficulty is to accept that we have chosen the wrong way but I can tell you will get benefice after have accepted.
Dear all, unexpectedly, I found this discussion site and read all answers. The question, “Why BCS theory of superconductivity can’t explain the behavior of HTSC like YBCO?” is very interesting but is old. Now, the meaning of the question is not maintained. BCS theory can explain the high Tc. In the BCS theory, a formula on the superconducting transition temperature was given as Tc=1.13EDexp(-1/N(0)V), where ED is the Debye cut-off energy, N(0) is the electronic density of states at the Fermi energy, V is the coupling potential of electron-phonon interaction. Superconductivity in inhomogeneous cuprates appears in the two dimensional CuO2 plane. The density of states in a 2 dimensional system is proportional to effective mass which diverges near the insulator-to-metal transition. The diverging effective mass can increase Tc in the formula. Actually, the effective mass was largely measured over 4 times of band mass. The effective mass increases, when electron-electron Coulomb interaction in a metal is large. Accordingly, the Coulomb interaction can be a cause of high-Tc even in the electron-phonon interaction [Article Analysis of the diverging effective mass in YaBa 2 Cu 3 O6+x...
]. Also, the coupling constant of b=2(gap)node/kBTc has a value near, less the BCS criterion (b=3.5) or a little bit high value, because the superconducting intrinsic gap is the nodal superconducting gap [Article Analyzing Intrinsic Superconducting Gap by Means of Measurem...
;Article Comments on identity of gap anisotropy and nodal constant Fe...
]. Many researchers have believed that the pairing symmetry of the inhomogeneous cuprate superconductors has dx2-y2-wave pairing symmetry with an electronic structure of clover, and that the superconducting intrinsic true gap exists at the antinode without the nodal superconducting gap. Experimental results have not proved the d-wave pairing symmetry although many experiments seem to show evidence of d-wave pairing symmetry. This is the biggest fallacy and an obstacle to see the truth. When the experiments proposed as evidence of d-wave are in detail analyzed, the experiments or their results had a defect. The investigation of the defect illuminated that evidence of d-wave symmetry came from pseudogap phase or flux trap [Article High-$T_c$ mechanism through analysis of diverging effective...
]. The insulator phase just before becoming a metal phase for superconductors is pseudogap phase with dx2-y2-wave pairing symmetry. As doping is given near the insulator-metal transition (IMT) or the metal-insulator transition (IMT), the IMT occurs at node; this is called the d-wave IMT or MIT gap [Article Analyzing Intrinsic Superconducting Gap by Means of Measurem...
(see line 16 to 15 from bottom at right column in page 2);Article Comments on identity of gap anisotropy and nodal constant Fe...
]. Then, free carriers are produced at the nodes and form the superconducting gap at node. Whereas the superconducting antinode gap is not formed, because antinode has no carriers due to absence of the IMT at the antinode. The superconducting gap is first formed at node and develops to antinode with increasing doping. Finally, the superconducting gap becomes the s-wave gap like ring in the optimally or overdoped regime. Therefore, the cuprate superconductor is s-wave superconductor. This was already experimentally proved. In conclusion, the inhomogeneous cuprate superconductors are composed of the d-wave pseudogap phase and the metal phase in the normal state. The pseudogap with d-wave symmetry undergoes the IMT and the metallic phase becomes the s-wave superconductor. The most important concept is the d-wave IMT which was first disclosed in [is called the d-wave IMT or MIT gap [Article Analyzing Intrinsic Superconducting Gap by Means of Measurem...
(see line 16 to 15 from bottom at right column in page 2);Article Comments on identity of gap anisotropy and nodal constant Fe...
]. Serially, research papers were announced [Article Explanation of small I_cR_n values observed in inhomogeneous...
;Article High-$T_c$ mechanism through analysis of diverging effective...
] and the public relation was given in internet [type in google, "How-do-Fermi-arcs-form-in-superconductors?"; type in google, "Why-is-the-superconducting-node-gap-observed-in-ARPES-spectra-of-cuprate-superconductors-?"]. Frankly speaking, a secret of high-Tc superconductivity has already been revealed. Thank you for attention. Yours Sincerely, Hyuntak. April 6, 2018.
With high-Tc superconductivity it was really a surprise for many people to discover oxygen 2p holes. For me it was a confirmation of my work “Crystal structures bonds” where I already suppose such 2p holes in 1983. This is also to be expected from the theoretical and experimental magnetic moments as explained in “Total angular momentum and atomic magnetic moments”. In this work each electron behaves as if it belong to a hydrogen like atom. As a chemist these different results allow me to propose some interpretations of the crystal structures in “Atoms and crystal structures” in 2009.
Now the rare gas compounds allow some new properties of valence. We know that the rare earth elements have mainly the valence three, a situation very different of that of the 3d elements which exhibit various possibilities. To understand this difference, we have to discuss the origin of the valence three of the rare earths. The two first valence states of the lanthanum have the same origin than the barium, element just before lanthanum. They are the result of the two 6s electrons appearing after the xenon. On the other hand the filling of the 4f shell starts after those of the 5s, 5p, 4d and 6s shells that is an amount of twenty electrons. Then it seems difficult to involve a 4f electron which is protected by all these electrons to explain the valence three of La. It is for this reason that in the old text books, the additional electron appearing with the lanthanum is supposed to be a 5d electron and also for some other elements of the rare earths. This hypothesis is now more or less forgotten but not fully. Considering the corpuscular model "Quantum State and Periodicity" an alternative approach is to suppose that it is the xenon shell, with its electrons gravitating in different directions of possible bonds, which leads to the third valence state of the Ln. This explains that in the high-Tc superconductors it is possible to replace La with Ba.
Now with Ba replacing La, there are defects in the corresponding bonds. These defects introduce lower gap for the conduction electrons, then the conductivity and the superconductivity. Indeed there are very few place for the conduction electrons to be trapped, as a result very a large mean free path.
Dear all:
Let me discuss once again the notion of free conduction electrons.
In the early part of the twenty century the electrons of the conduction were thought as free. This is quite evident when current flow is established. However, it is also important to be able to describe conduction electrons in the absence of current flow.
At this time the notion of gap was not yet so well established as now.
In a solid there are correlations between the positions of different conduction electrons, which minimize their repulsive interactions. A simple solution to describe these correlations is to suppose that each conduction electron, at low temperature and in the absence of current flow, belongs to one atom. This implies that there is a gap, which localizes conduction electrons when there is no external interaction, which may free them. See “Conductivity and statistics, an alternative view”.
In fact the notion of free electron was suggested in view to be able to use the statistical approach of the gas. Unfortunately the heat capacity of the conduction electrons does not confirms this hypothesis.
The difficulty is that the notion of heat was not yet very well grasp. As a result the notion of statistical weight was not use and the fact that the mean thermal energy must correspond to the maximum of this statistical weight was not introduce. This hypothesis allows to propose a more complete statistical distribution of the thermal energy see “Perturbations and Statistical Distribution of the Thermal Energy”.
You have there, I think, important difficulties to understand the conductivity and the superconductivity.
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