Normally condensed matter theories statisfy hole electron symmetry. This is because this symmetry is present in the underlying basic theories. But experimentally it is known that the phenomenon of superconductivity is hole electron asymmetric. Can we not then discard all the theories of superconductivity that are hole-electron symmetric? Is BCS a hole-electron symmetric theory?
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A possible starting point :
http://physics.ucsd.edu/~jorge/hole.html
(with only 115 references ... Good luck !)
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Lida: I would very much like to know the up-do-date information about the superconductivity in graphene? Has it been proved really that graphene is superconducting? If so what is the transition temperature? Is graphene magnetic as well? Can you give me some references?
Clerot: I looked at the like you gave. It has some useful information. I must go through it. Thanks very much.
I checked and found that BCS theory is hole-electron symmetric. If it really so then I guess one could rule out this theory for a valid theory of superconductivity. We can safely assume that Nature will not choose to generate this unique emergent phenomenon in condensed matter physics by several different ways. There should be a mechanism that explains superconductivity in all known superconducting materials. BCS is not capable of doing this and it seems it cannot even explain all properties even conventional superconductors. Someone must come out with the real theory of superconductivity. A century has already passes after the first discovery of superconductivity!
Hi Tapan,
This is a really great question, and I also believe it to be central to understanding the High-Tc cuprates, though perhaps less relevant to other superconductors. You might be surprised that in general, it is HARD to create a model in which there is electron-hole symmetry. Superconductivity is a special case in that the formation of Bogoliubov Quasiparticles creates a particle-hole symmetry. This symmetry only extends an energy scale of the order parameter. Thus, the system is not symmetric at high energies.
As far as I am aware, the most relevant paper showing particle-hole asymmetry in the cuprates is from Hashimoto et al. (http://www.nature.com/nphys/journal/v6/n6/full/nphys1632.html). But this is an effect which is due to a particle-hole asymmetric pseudogap. In fact, there are some subsequent works which I can share with you where additional features are seen which are consistent with
- particle-hole asymmetric pseudogap
- particle-hole symmetric BCS-like superconductivity (Bogoliubov Quasiparticles, in the same sense as in a simple BCS theory)
Please let me know if you are referring to some other experimental work which shows asymmetry due to the actual superconducting state. My understanding of the current viewpoint is that the underlying normal state has strong asymmetries which cause the anomalous experimental results.
James: Thanks for your comments. J.E. Hirsch from UC San Diego has been discussing hole electron asymmetry for a long time. He has written an article in Phys. Scr. 80, 035702 (2009) questioning the validity of BCS even in conventional superconductors. (1) BCS fails to explain why superconductors invariably shows positive Hall coefficient (Chapnik's rule). (2) BCS fails to explain Tao effect (superconducting microparticles aggregate in strong electric field into balls of macroscopic dimensions). (3) It also fails to explain Heer effect (small Nb clusters at low temperature develop dipole moments). It is unable to explain the electromagnetic effects of rotating superconductor. (4) BCS is unable to explain Meissner effect. (5) If I am correct BCS is hole-electron symmetric contrary to experiments. So BCS can not explain even conventional superconductors. Also why should Nature choose to produce this unique emergent phenomenon by different mechanism (there exists many theories of superconductivity formulated to explain different classes of superconductors). Not a very happy situation indeed!
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"Also why should Nature choose to produce this unique emergent phenomenon by different mechanism (there exists many theories of superconductivity formulated to explain different classes of superconductors)."
Nature might have many tricks : the same happens to superfluidity of He3 (BCS interpretation) and He4 (BEC interpretation).
"Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful."
(in G. Box, N. Draper, Empirical Model Building and Response Surfaces, 1987)
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Nature seems to have many tricks more evident in biology perhaps. But history of science shows that when we really understand Her Mind then we find apparent different tricks are related and are probably the same.
I find it likely that we have a different definition of what BCS theory means. Perhaps this has evolved over time. I'm referring to the simplest computation, with no knowledge of pairing potential, where you have no material specific parameters. In this regard you produce universal behaviours. However, if you go look at a real material, OF COURSE you are going to find things which are not explained. This boils down to the assumptions made regarding pairing.
Even with these assumptions, one can find a lot in the High-Tc literature which supports simple BCS-like pairing which produces low energy particle-hole symmetry. For example, Phys. Rev. Lett. 90, 217002 (2003).
Again, I am not sure which experiments you are referring to which say that BCS theory being particle-hole symmetric is contradictory to experiments.
Yes I am not questioning the basic ingredients of BCS but I think that most likely the pairing is not phonon madiated. The experiments I talked about above are the examples where BCS fails to explain even conventional superconductors. In fact the above experimental results are true for all superconductors.
Coming back to hole electron asymmetry the main point is the Chapnik's rule. All superconductors have positive Hall coefficient in the normal state above Tc. If you look for a superconductors then first make sure it has hole carriers. This is the guiding experimental principle that works. BCS does help to find new superconductors.
I shall have to read the article you referred above.
It seems to me that simple BCS theory is not formulated to explain the above experiments. Keep in mind however that there is no requirement of the source of the pairing mechanism in order to apply a simple BCS theory. So the issue of phonons vs something else is a moot point. It is a simple constant attractive potential with a cutoff.
I am still perplexed by your comments regarding particle-hole symmetry in BCS theory. In BCS theory there is no requirement that the total number of electrons in the system match the number of holes in the system. Instead, for a small range of energies near to the fermi level, there is a mixing of particle and hole states which produces a symmetry, but only over a small energy range. I would say that BCS theory does not care about whether the normal state is particle-hole symmetric or not. So yes, BCS theory does not help you find any new superconductor, because it starts from a viewpoint that you already have an attractive interaction, and will be susceptible to cooper pairing. Again, no material specifics beyond the density of states at the fermi level, and the constant pairing strength.
Regarding Chapnik's rule. I am not previously familiar with it. If you look at recent Hall coefficient measurements in YBCO (Nature 450, 533 (2007)) you indeed see a positive hall coefficient above Tc. However, at low temperatures, when they apply large magnetic fields, the hall coefficient does not become positive in the magnetically driven normal state, it becomes negative. There are two ways to look at this:
1) chapnik's rule is invalid.
2) chapnik's rule is valid. Which means that the magnetically driven normal state below Tc is not the same as the normal state above Tc in absence of magnetic field.
The jury is still out on this.
Most the ideas that I attempted to transmit was taken from a few articles by J.E. Hirsch of UC SanDiego. Here are the articles: J.E. Hirsch: Phys. Scr. 80, 035702 (2009), PRB 68, 012510 (2003), In High-Temperature Superconductivity, ed. J. Ashkenazi, Plenum (1991) p. 295. I shall be pleased to hear your opinion about these articles.
. arXiv:1110.0227 [pdf]
On the possible common nature of the ground state in Cu- and Fe-based HTSCs
K. V. Mitsen, O. M. Ivanenko
Johan: In all superconductors above Tc the charge carriers are holes. Can we then assume that the charge carriers are also holes in superconducting state? If so why? Why not electrons?
According to my theory Cooper pair is incorrectly defined that is why we have difficulty in understanding superconductivity and zero resistance and preparing superconductivity at room temperature. Superconductivity is a macro-phenomenon and so is my theory suggested much earlier.
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