Why some metals are not superconductors?

[lamba89]

Hello,

I'm studying about superconductivity. So far I understand that the material needs have zero resistance and meissner effect to be a superconductor. But why materials such as copper or gold are not superconductors?

I think it's something to do with some quantum effect like cooper pairing but I can't find much details on it. Can someone please explain this to me.

Thanks

 

[Bloodthunder]

Taken from http://www.superconductors.org/TYPE1.htm#AuAgCu

 

[DrDu]

Whether a substance becomes superconductive at low temperatures or not depends on whether the attraction between the electrons due to the coupling to the lattice vibrations can outweight the repulsion of the electrons due to Coulombic repulsion at least for some frequencies. As shown in the explanation by Bloodthunder, the electron phonon interaction is weak in copper or gold so that Coulomb effects win and prevent superconductivity.

 

[M@2]

Why gold and copper are not superconductors?

why materials such as copper or gold are not superconductors?

I think it's something to do with some quantum effect like cooper pairing but I can't find much details on it.

It is one of the main puzzles in the theory of superconductivity. But it is true as experimental fact.

We may also ask why gold and copper are not high temperature superconductors?

Usual explanation for phonon superconductivity see in DrDu post. But it is very difficult to get and undestand the calculation of pairing in copper and gold.

Let us see on experiment facts.
1. Conventional superconductor: 96% hole superconductors (Chapnik rule).
2. HTSC: hole doped Tc much greater than electron doped Tc
3. Phase diagram of Tc and % of doping: concave, superconductor in a limited region of doping.
4. Homes scaling law:
Tc ~ const*(number of superconducting electrons)*(resistivity in normal state)

These experimental facts lead us to combine empirical rules:
Superconducting electrons are those, close to Fermi surface.
Superconducting electrons give gain in free energy and in gap
Nonsuperconducting electrons give antigain in free energy in superconducting state and give very low resistivity in normal state (highly overdoped materials are not superconductors).
Holes give additional gain in free energy for superconductors.

Combining the empirical rules for copper and gold we may guess why copper and gold are not superconductors:
Copper and gold don't have hole conductivity
Copper and gold have too much ordinary nonsuperconducting electrons and too big conductivity in normal state.
The gain in free energy from superconducting electrons can't compensate antigain from nonsuperconducting electrons and antigain of electron conductivity (hall constant <0).

 

[DrDu]

Although I am also not a specialist, here, I think that trnsition temperatures etc. can be fairly well be calculated for ordinary superconducting metals ab initio (E. g. solving Eliashberg equations, cf. http://www.ifw-dresden.de/institutes/itf/members/helmut/sc2.pdf). So the missing superconductivity of copper and gold is certainly not a mystery or a mere experimental fact.

 

[M@2]

Why gold and copper are not superconductors?

E. g. solving Eliashberg equations

solving ?
Do you mean fitting ?

Fitting with infinite number of fitting parameters.
Eliashberg function is a FUNCTION, so it consists of infinite number of values.
With infinite number of fitting parameters you can fit to any theory and get any result.
It is not convincingly for experimentalists.
It may be convicingly only for some theoreticians, who work with Eliashberg functions for different metals.

Where can we see theoretical explanation for Chapnik effect with Eliashberg function?
Where can we see theoretical explanation for Homes scaling law with Eliashberg function?
As we know Homes law is valid also for conventional superconductors.
http://www.nature.com/nature/journal/v430/n6999/full/nature02673.html

 

[DrDu]

With Eliashberg function, do you mean \alpha^2 F (\omega)? I thought, it can be calculated ab initio today (see my link to the paper of Eschrig), so without any parametrization involved, however, I don't know with what accuracy. It is clear, that an ab initio calculation does not a priori lead to insight into the mechanism of empirical laws.

 

[M@2]

Why gold and copper are not superconductors?

With Eliashberg function, do you mean \alpha^2 F (\omega)? I thought, it can be calculated ab initio today (see my link to the paper of Eschrig), so without any parametrization involved, however, I don't know with what accuracy. It is clear, that an ab initio calculation does not a priori lead to insight into the mechanism of empirical laws.

Yes, \alpha^2 F (\omega)

But let me explain more precisly. Consider http://iopscience.iop.org/1367-2630/11/12/125005/fulltext equation (2).

Equation (2) is exact.
But equation (3) is illegal from the point of quantum mechanics

What the hell do delta functions with epsilon and omega appeared from? This expression of Eliashberg function is absolutely incorrect. It is becouse (3) absolutely ignores virtual processess. But we know well that such processess are of vital importance in physics, see for example phase transition in Dicke model:
Hepp, Elliott Lieb „On the superradiant phase transition for molecules in a quantized radiation field: the Dicke Maser Model“, Annals of Physics Vol.76, 1973, pp.360-404
and one dimensional Frohlich theory of superconductivity of 1954y:
H Fröhlich 1961 Rep. Prog. Phys. 24 1
http://rspa.royalsocietypublishing.org/content/223/1154/296

So eq. (3) is approximate expression of the theory and must be considered as a postulate of phenomenological theory. It can't be considered as SOLVING, but it can be considered as FITTING function. Eq (3) defines cutoff parameter in ordinary theory, but is it sufficient to define ONLY cutoff parameter?

We must have calculation of contribution of neglected terms in eq. (3), especially for nonsuperconducting electrons (the number of nonsuperconducting electrons >> the number of superconducting electrons).

 

[f95toli]

I think that trnsition temperatures etc. can be fairly well be calculated for ordinary superconducting metals ab initio

Indeed, Tc and other parameters can be calculated from first principles for single elements as well as for binary compounds. The theoretical predictions are very accurate, even for complicated materials such as MgB2. As far as I know the only "in" data for the models are the elements and the crystal structure. And as far as I remember this is done using DFT combined with the Eliashberg equation (but I am not a theorist, so I might be wrong).

 

[M@2]

Why gold and copper are not superconductors?

Indeed, Tc and other parameters can be calculated from first principles for single elements as well as for binary compounds. The theoretical predictions are very accurate, even for complicated materials such as MgB2.

If it is true, why we can't discover another "MgB2" like superconductor (40K) and can't "calculate" empirical Chapnik and Homes's rules for coventional superconductors?

It is the illustration of Chapnic rule. The figure above shows a plot of the superconducting critical temperatures of the elements versus the inverse Hall coefficient. Note that superconductors are predominantly found among materials with positive Hall coefficient.

As i know main improvements in superconductivity theory were made AFTER unexpected results in experiments (for example zero isotopic effect in ruthenium, incorrect dependence of Tc(density of states), ...). Why?

Why advice to search superconductor among materials with high T_Debye is not working?

It is the illustration of Chapnik rule, Debye T and density of states. Element 2 is superconductor. Why?

As for MgB2: below left picture MbB2, right picture graphite
Pictures from the book: Electronic structure: basic theory and practical methods / Richard M. Martin 2004, page 48

We see as Chapnik rule works with exellence (red circles) for MgB2 and we see how we can make graphite HTSC by doping.

Empirical rules now more useful than theory.

 

[DrDu]

In respect to your post #8 I have the following commentary: The formula (3) is a Fermi Golden Rule type expression for the density of states although the formula you cited may contain other approximations (i.e. the use of the g's as defined in eq. 2), the representation of the density of states in terms of the delta functions is in principle exact. Cf. Eq. 2.9 and 2.17 in the lecture notes of Eschrig.

 

[M@2]

In respect to your post #8 I have the following commentary: The formula (3) is a Fermi Golden Rule type expression for the density of states although the formula you cited may contain other approximations (i.e. the use of the g's as defined in eq. 2), the representation of the density of states in terms of the delta functions is in principle exact. Cf. Eq. 2.9 and 2.17 in the lecture notes of Eschrig.

Yes, You are right, the representation of the density of states in terms of the delta functions is in principle exact. But Fermi golden rule is not exact.

When i read phrase "Fermi golden rule " (rate equation) i allways remember Tennis Davis Cup:
https://e-reports-ext.llnl.gov/pdf/246009.pdf
See page 6 (may be 5 depending on browser):

Davis was unconvinced, however, and on the spur of the moment offered a challenge, to be known as The Davis Cup, to anyone who could convince him that coherence was important in his job as leader of the LIS project.
Eventually, largely as the result of several years of collaboration between Joe and
Bruce, Davis acknowledged that it was indeed important to base modeling on the
Schr¨odinger equation rather than rate equations, and he graciously made an award
of The Davis Cup (to BWS).

I think, superconductivity physics needs next challenger to offer Supercondictivity Cup, that phonon coherence is important to superconductivity.

I can't imagine that incoherent phonons with the help of random phrase approximation formulas can make superconducting electrons coherent .

LIS=Abstract:This article summarizes the developing understanding of coherent atomic excitation, as gained through a collaboration of J.H. Eberly with the Laser Isotope Separation Program of the Lawrence Livermore National Laboratory, particularly aspects of coherence, population trapping, multilevel multiphoton excitation sequences,analytic solutions to multistate excitation chains,the quasicontinuum, pulse propagation, and noise. In addition to the discovery of several curious and unexpected properties of coherent excitation, mentioned here, the collaboration provided an excellent example of unexpected benefits from investment into basic research.
c 2001 Optical Society of America

 

[DrDu]

I can't imagine that incoherent phonons with the help of random phrase approximation formulas can make superconducting electrons coherent .

Who sais so?

 

[M@2]

Who sais so?

This phrase is mine. I can repeat it:
I can't imagine that incoherent phonons with the help of random phrase approximation formulas can make superconducting electrons coherent .

I worked 3 years in laser laboratory at the beginning of 1970-1980. We have the best equipment in the USSR and may be the best in the world those years. Dilemma of rate equation (Fermi golden rule) and time dependent Shroedinger equation was solved by us several years before Davis challenge. So i can repeat in accordance with final Davis opinion: Fermi golden rule may by wrong in practice. So Eliashberg equation may be misleading. Especially when amplitudes of phonon modes are very greate and don't determined only by temperature. Consider the opportunity of phonon superradiance, for example.

The main problem in superconductivity, to my mind, is not gap or pairing. The main problem is the origin of electron gas coherence.

 

[DrDu]

Yes, I had already the impression that it was your phrase. But do the Eliashberg equations really encompass a random phase approximation for the phonons? I can't say.

 

[M@2]

But do the Eliashberg equations really encompass a random phase approximation for the phonons? I can't say.

When we get Fermi golden rule we do 2 things: all states except initial one are unoccupied, we make derivative in time.

It is evident that these initial conditions can't be preserved in time. We have two possibility to solve equation: honest and unhonest one.

Honest is integration in time and take into account level occupancy.

Unhonest is to postulate that level occupancy wave functions are in random phase and to make calculation easy.

Sometimes goal justifies the means, sometimes not.

Yasha Eliashberg is of Lev Landau "school of physisists". This school is famous for exellent theoretical explanations of ALREADY KNOWN experimental results. But i hardly remember when they SUCCESSFULLY PREDICT results for UNDONE EXPERIMENTS, except Abrikosov vortex and supersolid He4 by Andreev et al.

When you know the end result it is much more easier to make approximation in "true" direction.

 

[DrDu]

You seem to be a russian heretic!
After all, Landau was in charge of the numerical computations of the russian hydrogen bomb and got two Stalin prizes for it. So he was involved in dirty applied weapon projects, too.

 

[M@2]

We in USSR had two personality cults:
1. Stalin personality cult
2 And in physics Lev Landau personality cult

But we should know that there were in USSR other first class physisists: Vladimir Fock, NN Bogoliubov, E I Tamm, Vlasov (plasma),...
I had the honor to be near Fock for several years, but not acquainted with. He was almost deaf from the First World War as being in artillery, i tryed several times speak to him, but almost in vain. Fock made it possible for us (students) to get PhysRev from his library. It was very generous.

Landau has made useful work in USSR nuclear program, but there were scientist much more involved in program.
Atomic bomb program is considered in USA, that we spyed ALL secrets from Los Alamos. I should say that only two person knew spyed documents: KGB leader Beria and Kurchatov. No one else knew, that we have spyed documents.

Hydrogen bomb was created by us independently from USA and MOBILE hydrogen bomb was exploded in USSR earlier than in USA. The main scientists (ideas) in hydrogen bomb were Saharov and Nobel Prize winner (2003) Ginzburg (to use Lithium). But the honor of creating hydrogen bomb belongs mainly to Beria and Kurchatov.

Lev Landau did not most impotant works in bomb projects, but helper works.
Almost all participants have got various prizes.

 

[DrDu]

Yes, that with the personality cult around Landau is certainly true. I heard some lectures of his old fellows who all were proud to tell some anecdotes about Landau.
I am from Germany, so you don't have to convince me that all of nuclear technology hasn't been spied from US, e.g. uranium centrifuges, which are more economical and technically feasible than laser separation, have been developed by German war prisoners and soviet scientists. (And later been patented in the west once the Germans were allowed to return).

I suspect that Landau, Ginzburg etc. where happy to avoid being forced to work in atomic bomb programs, that's maybe why they tried to avoid too applied science in general.
When I was taking theoretical solid state physics long ago, my professor pointed out to us that the Russians were very close to find a theory of superconductivity when the paper of BCS appeared, but that they had relied to long on Migdal's theorem which breaks down in superconductors, and which wasn't that known outside USSR at that time.

 

[ZapperZ]

Let's not derail this thread into a history of Soviet physics.

Zz.

 

[M@2]

Indeed, Tc and other parameters can be calculated from first principles for single elements as well as for binary compounds. The theoretical predictions are very accurate, even for complicated materials such as MgB2. As far as I know the only "in" data for the models are the elements and the crystal structure. And as far as I remember this is done using DFT combined with the Eliashberg equation (but I am not a theorist, so I might be wrong).

If we see another thread How to solve Eliashberg Equations? it is a little bit doubtfully.

We don't know not only programm code, but even description of input data.
Be there program code i could verify that suggestion, that Eliashberg equation can give opportunity to accurately calculate superconductor parameters ab initio.

I hardly believe it. Can you give article reference?

Were calculations made AFTER or BEFORE experiment?

Do You claim that we can predict the superconductivity or nonsuperconductivity of all elements and simple alloys?

 

[f95toli]

Just of a google search for first principle calculations of for example MgB2. Yes, the calculations were done after the discovery of superconductivity in MgB2, but once found it only took the theory groups a couple of weeks to do the calculations (I was involved in some work in Josephson junction in MgB2 the first months after its discovery to I went to a few meetings where this was discussed).
Note that whereas MgB2 is a BCS superconductor, it is nevertheless quite complicated (double gap structure etc), so it is quite impressive how well the calculations agreed with the experimental data.

 

[M@2]

OK. I googled out. And found a lot of referencies, which gave almost nothing, words only, that calculations are in good agreement with theory (supposed with BCS?).
But where is concrete calculations and algorithms?
Does the SAME PROGRAM can PREDICT not only MgB2 parameters, but Ruthenium, for example? Isotopic effect? Is programm cutoff CALCULATED or FITTED to omega_Debye? What is the error? Was the GOOD result of calculation accidental ore not?
I suppose we don't want to have different theories for different elements.

I already wrote in this thread, that empirical rules are very good for conventional superconductors. Which theory can give the best results for them?

I know only one theory, which can, in principle, give naturally coherence to electrons, explain Chapnik and Homes's rules, isotopic effects, one half flux quantization, energy gap. It is the Frohlich theory of superconductivity, corrected, quantized and extended to 3d case:
http://rspa.royalsocietypublishing.org/content/223/1154/296.short

And, by the way, can in principle explain why Cu, Ag, Au are not superconductor. Becouse they have too many electrons, and phonons can't directly trasfer electrons at fermi level to opposite side of Fermi surface (phonons maximum wave vector is too small).

 

[ZapperZ]

OK. I googled out. And found a lot of referencies, which gave almost nothing, words only, that calculations are in good agreement with theory (supposed with BCS?).
But where is concrete calculations and algorithms?
Does the SAME PROGRAM can PREDICT not only MgB2 parameters, but Ruthenium, for example? Isotopic effect? Is programm cutoff CALCULATED or FITTED to omega_Debye? What is the error? Was the GOOD result of calculation accidental ore not?
I suppose we don't want to have different theories for different elements.

I already wrote in this thread, that empirical rules are very good for conventional superconductors. Which theory can give the best results for them?

I know only one theory, which can, in principle, give naturally coherence to electrons, explain Chapnik and Homes's rules, isotopic effects, one half flux quantization, energy gap. It is the Frohlich theory of superconductivity, corrected, quantized and extended to 3d case:
http://rspa.royalsocietypublishing.org/content/223/1154/296.short

And, by the way, can in principle explain why Cu, Ag, Au are not superconductor. Becouse they have too many electrons, and phonons can't directly trasfer electrons at fermi level to opposite side of Fermi surface (phonons maximum wave vector is too small).

Your posts is making less and less sense. Now you're citing a 1D electron gas SPECIAL CASE and claim that it can explain everything!

The phonon spectrum is TOTALLY SEPARATE from superconductivity, because it is a physical characteristics of the material. Based on such phonon spectrum, be it either experimental or theoretical, one can THEN feed it into the BCS theory and calculate Tc. That is why, knowing the phonon spectrum and coupling strength of conventional metals, it was thought that the highest Tc one could get out of these materials is around 25K. How else can one make such predictions if these things are not known? Furthermore, tunneling spectroscopy of conventional superconductors produces the same characteristics coupling that matches the phonon normal modes. Along with the isotope effect, these two produced very convincing evidence for such phonon coupling.

The ruthenates, cuprates, pnictides, etc. are of completely different beasts. The cuprates, for example, may still have phonons as the coupling mechanism. This is because the apical oxygen could produce the half-breathing mode that can produce pairing at Tc at such high temperatures. So there is still the possibility (even though I don't buy it) of phonons being responsible for such pairings.

If you think such-and-such a theory can supersede BCS, and if you think you can explain all of superconductivity in all these material, this is the WRONG place for you to make such a claim. Go to Nature, and publish it. Till then, please cease from making such a claim or you will be in violation of the rules of this forum that you had agreed to.

Zz.

 

[Physics Monkey]

OK. I googled out. And found a lot of referencies, which gave almost nothing, words only, that calculations are in good agreement with theory (supposed with BCS?).
But where is concrete calculations and algorithms?
Does the SAME PROGRAM can PREDICT not only MgB2 parameters, but Ruthenium, for example? Isotopic effect? Is programm cutoff CALCULATED or FITTED to omega_Debye? What is the error? Was the GOOD result of calculation accidental ore not?
I suppose we don't want to have different theories for different elements.

I already wrote in this thread, that empirical rules are very good for conventional superconductors. Which theory can give the best results for them?

I know only one theory, which can, in principle, give naturally coherence to electrons, explain Chapnik and Homes's rules, isotopic effects, one half flux quantization, energy gap. It is the Frohlich theory of superconductivity, corrected, quantized and extended to 3d case:
http://rspa.royalsocietypublishing.org/content/223/1154/296.short

And, by the way, can in principle explain why Cu, Ag, Au are not superconductor. Becouse they have too many electrons, and phonons can't directly trasfer electrons at fermi level to opposite side of Fermi surface (phonons maximum wave vector is too small).

Perhaps you will find these to your liking? They are one example among many of ab initio attempts to predict superconducting properties. It is a series of three papers:

http://arxiv.org/abs/cond-mat/0408685 explains the basic formalism

http://arxiv.org/abs/cond-mat/0408686 applies the formalism to elemental metals

http://arxiv.org/abs/cond-mat/0408688 applies the formalism to MgB2

I haven't studied these particular works in detail, but they seem to represent the kind of presentation you are interested in.

Hope this helps.

 

[M@2]

ZapperZ, i am condused.

I used words: "in principle". And i am not an author of any theory of superconductivity. But can i discuss published papers and have the opinion about them?

Your posts is making less and less sense. Now you're citing a 1D electron gas SPECIAL CASE and claim that it can explain everything!

To be precise i don't claim the theory of everything. I only expressed my opinion about Frohlich 1d theory, elementaryly extended to 3d BCS like case. BCS paper was of spherical Fermi surface. It is elementarily 1d Frohlich case extend to 3d with 3d spherical Fermi surface and 3d spherical combination of phonons modes combined in one phonon mode, corresponding to Kohn anomalies (full nesting).
By the way there is interesting experimental paper:
Energy Gaps and Kohn Anomalies in Elemental Superconductors
http://www.sciencemag.org/content/319/5869/1509.abstract
http://elib.uni-stuttgart.de/opus/volltexte/2009/3962/

The Calculations almost the same as in original Frohlich paper. As to quantization. Till now we use Frohlich quantized hamiltonian.

The phonon spectrum is TOTALLY SEPARATE from superconductivity, because it is a physical characteristics of the material. Based on such phonon spectrum, be it either experimental or theoretical, one can THEN feed it into the BCS theory and calculate Tc. That is why, knowing the phonon spectrum and coupling strength of conventional metals, it was thought that the highest Tc one could get out of these materials is around 25K. How else can one make such predictions if these things are not known? Furthermore, tunneling spectroscopy of conventional superconductors produces the same characteristics coupling that matches the phonon normal modes. Along with the isotope effect, these two produced very convincing evidence for such phonon coupling.

I want compare BCS prediction and Frohlich's, why not?

The ruthenates, cuprates, pnictides, etc. are of completely different beasts. The cuprates, for example, may still have phonons as the coupling mechanism. This is because the apical oxygen could produce the half-breathing mode that can produce pairing at Tc at such high temperatures. So there is still the possibility (even though I don't buy it) of phonons being responsible for such pairings.

There was recent paper R. He, et al., Science 331, 1579 (2011)
May be i don't understand, but the paper closes the problem of paring of electrons between pseudogap Tp and superconducting Tc.

It is indicative how incorrectly we may be deceived by seemed pairing.

If you think such-and-such a theory can supersede BCS, and if you think you can explain all of superconductivity in all these material, this is the WRONG place for you to make such a claim. Go to Nature, and publish it. Till then, please cease from making such a claim or you will be in violation of the rules of this forum that you had agreed to.

Zz.[/QUOTE] This is not the case i think about. I think about origin of coherence of electrons. Can You help me?

 

[ZapperZ]

ZapperZ, i am condused.

I used words: "in principle". And i am not an author of any theory of superconductivity. But can i discuss published papers and have the opinion about them?
To be precise i don't claim the theory of everything. I only expressed my opinion about Frohlich 1d theory, elementaryly extended to 3d BCS like case. BCS paper was of spherical Fermi surface. It is elementarily 1d Frohlich case extend to 3d with 3d spherical Fermi surface and 3d spherical combination of phonons modes combined in one phonon mode, corresponding to Kohn anomalies (full nesting).
By the way there is interesting experimental paper:
Energy Gaps and Kohn Anomalies in Elemental Superconductors
http://www.sciencemag.org/content/319/5869/1509.abstract
http://elib.uni-stuttgart.de/opus/volltexte/2009/3962/

The Calculations almost the same as in original Frohlich paper. As to quantization. Till now we use Frohlich quantized hamiltonian.
I want compare BCS prediction and Frohlich's, why not?

There was recent paper R. He, et al., Science 331, 1579 (2011)
May be i don't understand, but the paper closes the problem of paring of electrons between pseudogap Tp and superconducting Tc.

It is indicative how incorrectly we may be deceived by seemed pairing.

Your post is all over the place. I don't even know anymore what it is that you're arguing. BTW, BCS theory CAN and has been shown to also work with non-spherical Fermi surface. As long as you have the correct band structure of the material, it works! The overdoped cuprates have properties that follow mean-field approximation, and have clear Landau's quasiparticle behavior. Thus, BCS theory works quite well there!

If you have a chip on your shoulder and want Frolich to get the recognition that has eluded him, more power to you. Then you should post in the politics forum, not in physics.

The papers you cited have done nothing to clarify your stand. In fact, I would say the Science paper from the Keimer's group clearly shows how the phonon structure is responsible for many of the observed properties. Thus, your question earlier on the role of phonons in superconductivity is clearly addressed by such a paper, whether you consciously realize it or not.

Zz.

 

[M@2]

Perhaps you will find these to your liking? They are one example among many of ab initio attempts to predict superconducting properties. It is a series of three papers:

http://arxiv.org/abs/cond-mat/0408685 explains the basic formalism

http://arxiv.org/abs/cond-mat/0408686 applies the formalism to elemental metals

http://arxiv.org/abs/cond-mat/0408688 applies the formalism to MgB2

I haven't studied these particular works in detail, but they seem to represent the kind of presentation you are interested in.

Hope this helps.

Excuse me please.
I read the abstract of the first paper:

Ab-initio theory of superconductivity - I: Density functional formalism and approximate functionals

Do You consider, that i, as the representative of Fock school, don't know the quantum mechanics fundumentals? Before Kohn-Sham equations there were Hartree Fock equations. And do You imagine, that Fock (or Ludwig Faddeev ore my curator Mercur'ev) could use diagrammatical methods? They made more fundamental tasks, conserving invers problem method. Diagrammatical method You can send to elementary school pupils. Excuse.

The formula of approximate theory could approve nothing.

 

[M@2]

Your post is all over the place.
Excuse, i has a very poor english language. I had never been outside former USSR. My work was extreemly classified. And i had never used spied information. My brain is more useful than spied reports. So i coudn't realize what do You mean.

I don't even know anymore what it is that you're arguing. BTW, BCS theory CAN and has been shown to also work with non-spherical Fermi surface. As long as you have the correct band structure of the material, it works! The overdoped cuprates have properties that follow mean-field approximation, and have clear Landau's quasiparticle behavior. Thus, BCS theory works quite well there!

Imagine that Yours words are true. Non-spherical Fermi surface is the next step to analyse. But we want that every student of the age of 10 could understand the superconductivity theory. What if we will see that Frohlich theory works quite well?
There were in history such events (Koprnicus Ptolemeus).

If you have a chip on your shoulder and want Frolich to get the recognition that has eluded him, more power to you. Then you should post in the politics forum, not in physics.

It is your opinion, not mine. I now don't involved in politics.

The papers you cited have done nothing to clarify your stand. In fact, I would say the Science paper from the Keimer's group clearly shows how the phonon structure is responsible for many of the observed properties. Thus, your question earlier on the role of phonons in superconductivity is clearly addressed by such a paper, whether you consciously realize it or not.

I as Kapitsa consider the experiment as diamond, more precious than any theory. The experiment says: there are two phase transitions. Pseudogap is dielectric gap, depending of wave vector. Superconductor gap could not be nonzero if pseudogap is <> 0. So SC and Rseudo gaps coexist, but in different direction of of wave vector.
Zz.[/QUOTE]

 

[M@2]

If you think such-and-such a theory can supersede BCS, and if you think you can explain all of superconductivity in all these material, this is the WRONG place for you to make such a claim. Go to Nature, and publish it. Till then, please cease from making such a claim or you will be in violation of the rules of this forum that you had agreed to.Zz.

And You will give the order to Russia security service that my paper can be disclosed to everybody in the world...

Do You live in real world? Did You worked in Los Alamos?

A friend of mine published 2-3 papers a year in PhysRev till 2003.

Now nothing!
As he explained to me, he works for NASA and there was the condition that nothing could be published during his trade contract.

Why don't you buy a plane?
My salary is 100 bucks a month...
Does such salary exist?
In Russia you don't have salary in any case.
So we all go to Gaddaphi and make ALL france airplane down in a week.
[PLAIN]http://img.beta.rian.ru/images/30560/65/305606503.jpg
Do You see the rocket?
Votkinsk was the place where i met an american in the cafe for the first time in my life.
They wanted to know the diameter of our rockets.
And it is the birthplace of our worldknown composer Piotr Chyikovski (his farther was the main director of the plant before the 1917 revolution).
And there were my golden days.

 

[M@2]

I feel, i was too curt in my posts. I ask to forgive me this.
Physics Monkey, thank You for your help.

 

[M@2]

Why some metals are not superconductors? Quantum 1D wires

Frohlich and BCS theory can be compared in 1d and quasi 1d objects: quantum wires, chaines of quantum dots, quasi-onedimentional metals, nanotubes.

The most decisive experiment can be: search for superradiant phonons near Kohn anomaly or measurement of lifetimes of phonons near Kohn anomaly , which can be dissipated by superradiant phonons.

I will try to convince some people from Chernogolovka institutes of Russian Academy of Sciences to realize such an experiment.

It is a pity that such experiments were never done, except already mentioned:
Energy Gaps and Kohn Anomalies in Elemental Superconductors
http://www.sciencemag.org/content/31.../1509.abstract
http://elib.uni-stuttgart.de/opus/volltexte/2009/3962/

 

[DrDu]

The superconducting phase (broken gauge symmetry) is a different phase from the normal phase. However, systems with a broken continuous symmetry are only possible in at least 3 dimensions. So while BCS and Froehlich theory may nevertheless predict interesting phenomena in 1-d systems, they cannot predict superconductivity.

 

[ZapperZ]

I as Kapitsa consider the experiment as diamond, more precious than any theory. The experiment says: there are two phase transitions. Pseudogap is dielectric gap, depending of wave vector. Superconductor gap could not be nonzero if pseudogap is <> 0. So SC and Rseudo gaps coexist, but in different direction of of wave vector.
Zz.

This is VERY confusing.

The pseudogap in the normal state of the cuprates is not simply a "dielectric gap". The transition at T* is actually a transition to a non-superconducting broken symmetry state. The dielectric gap is simply a gap in the single-particle state.

Whether the pseudogap state is a precursor or in competition with superconductivity is still being debated. See R.-H. He et al., Science v.331, p.1579 (2011).

Furthermore, the superconducting gap is not symmetric over the Fermi surface, since it has a d-wave symmetry. The nodal direction has no gap. Your claim that both gaps they are different in different direction needs experimental verification.

Zz.

 

[M@2]

The superconducting phase (broken gauge symmetry) is a different phase from the normal phase. However, systems with a broken continuous symmetry are only possible in at least 3 dimensions. So while BCS and Froehlich theory may nevertheless predict interesting phenomena in 1-d systems, they cannot predict superconductivity.

Mathematics says: it is forbidden by theorem. Physics says: let us try.

Graphene is an example. Physisists can a little bit change the condition of the theorem in experiment and theorem does not hold.

 

[M@2]

The pseudogap in the normal state of the cuprates is not simply a "dielectric gap". The transition at T* is actually a transition to a non-superconducting broken symmetry state. The dielectric gap is simply a gap in the single-particle state.

I hardly interested in using group theory in physics. So higgs boson or spontaneously broken symmetry in my mind add nothing to my physical essence of the processes. Usually i ask myself: what will happen, if we have no symmetry from the beginning and there is no symmetry to be broken?

Next. Is "non-superconducting broken symmetry state" one electron states? I image that it is the one electron states where some states have gap in the direction of the wave vector and some states have no gap in the direction of the wave vector.

Dielectric gap means that all possible states in this direction are busy and the highest in energy level is lower than Fermi energy.
In polar coordinates (direction, pseudogap value) it is 4 petals. If we diminish doping, petals become wider and longer and at some nonzero doping sample can become insulator.

Whether the pseudogap state is a precursor or in competition with superconductivity is still being debated. See R.-H. He et al., Science v.331, p.1579 (2011).

Furthermore, the superconducting gap is not symmetric over the Fermi surface, since it has a d-wave symmetry. The nodal direction has no gap. Your claim that both gaps they are different in different direction needs experimental verification. Zz.

I think superconductor petals and PG petals couldn't overlap for T<Tsc. So you can verify experimentally nonoverlapping.

So for underdoped cuprates we can suspect 8 SC petals, for overdoped 4 SC petals. In principle SC petals can themselves overlap and we may have nonzero SC gap in nodal directions.

You are quite right, ZapperZ, that we need more experimental results.

 

[ZapperZ]

I hardly interested in using group theory in physics. So higgs boson or spontaneously broken symmetry in my mind add nothing to my physical essence of the processes. Usually i ask myself: what will happen, if we have no symmetry from the beginning and there is no symmetry to be broken?

Next. Is "non-superconducting broken symmetry state" one electron states? I image that it is the one electron states where some states have gap in the direction of the wave vector and some states have no gap in the direction of the wave vector.

I have no idea what you just said here.

Furthermore, just because there is a "gap", it doesn't mean that it is the SAME gap, or it is a generic gap. A spin gap is certainly different than an electronic gap.

Dielectric gap means that all possible states in this direction are busy and the highest in energy level is lower than Fermi energy.
In polar coordinates (direction, pseudogap value) it is 4 petals. If we diminish doping, petals become wider and longer and at some nonzero doping sample can become insulator.

Er... huh?

I think superconductor petals and PG petals couldn't overlap for T<Tsc. So you can verify experimentally nonoverlapping.

So for underdoped cuprates we can suspect 8 SC petals, for overdoped 4 SC petals. In principle SC petals can themselves overlap and we may have nonzero SC gap in nodal directions.

You are quite right, ZapperZ, that we need more experimental results.

You have not shown any experimental papers on your "8 petals". Maybe this came out of your "secret" Soviet research that never got published?

Zz.

 

[M@2]

You have not shown any experimental papers on your "8 petals". Maybe this came out of your "secret" Soviet research that never got published? Zz.

I think, that you know better about experimental results. At least two recent (2007-2011) papers in Nature or Science, i have seen, pictures 3d plot of two different gaps. 2 "3d petals" in the plot myltiplyied by 4 gives 8.

I'll give the reference later, excuse. Unfortunatly i am repairing Windows now and can't use Yandex or Google personal searches on my computer. After repairing i'll index my Science directory. But it has a lot of books (40 000) and scientific papers (1 000 000), so it'll be the long process

Last time Yandex indexed 965 000 of text type documents, but it took 2 weeks ( i have no a supercomputer).

 

[ZapperZ]

I shall await for your references.

In case you missed it, I've already given, in Msg. #34, a citation to a recent Science paper that indicated two different gaps coexisting in the cuprates. So this is NOT a mystery, but the nature of the pseudogaps is still HIGHLY DEBATED and not a done deal. It means that you are overstating the certainty of its nature.

Zz.

 

[M@2]

ZapperZ, thank You.
Let us see for example http://www.nature.com/nature/journal/v450/n7166/fig_tab/nature06219_F4.html#figure-title

As we know superconducting gap depends firmly on temperature.
Pseudogap don't depend on temperature very much
So points on the plot near antinodal belongs exclusivly to pseudogap.
But where does begin superconducting petal?

This demands special fitting, but that was not done.
It may be needs additional experiments to distingwish SC gap and PG gap

PS. I also mentioned He at al

There was recent paper R. He, et al., Science 331, 1579 (2011)
May be i don't understand, but the paper closes the problem of paring of electrons between pseudogap Tp and superconducting Tc.

 

[ZapperZ]

ZapperZ, thank You.
Let us see for example http://www.nature.com/nature/journal/v450/n7166/fig_tab/nature06219_F4.html#figure-title

As we know superconducting gap depends firmly on temperature.
Pseudogap don't depend on temperature very much
So points on the plot near antinodal belongs exclusivly to pseudogap.
But where does begin superconducting petal?

This demands special fitting, but that was not done.
It may be needs additional experiments to distingwish SC gap and PG gap

PS. I also mentioned He at al

I'm familiar with this. So how is this similar to what you mentioned? I don't see any "8 petals".

Furthermore, the pseudogap IS tied to temperature. It just that it persists even higher than Tc. Tunneling spectroscopy measurements have shown that to be the case. See N. Miyakawa et al. PRL 83, 1018 (1999), for example.

This is all fun and dandy, but I'm at a loss as to how this has any bearing on your original intention in this thread. How does this relates to not being able to use First Principles in deriving Tc and denoting which material can become a superconductor? What point are you trying to make here?

Zz.

 

[M@2]

The plot clearly shows, that near antinodal direction everybody can see part of pseudogap petal without mixing with superconducting petal.
Near nodal direction everybody can see part of superconducting petal without mixing with pseudogap petal. The most indicator: temperature dependence. The authors, i think, should try fitting with nonoverlapping SC and PG petals. At the angle where PG becomes zero (ie dissappear) the SC gap begins to appear and must be in maximum (remember empirical Chapnik rule). Though transfer region PGpetal --->SCpetal can be more complex, PG is not obligatory became zero in this region. It can be changed by SC petal without PG being zero.
They are compete in this region of angles for minimum of free energy

Furthermore, the pseudogap IS tied to temperature

Yes, of course, but the value of PG gap don't go to zero even at T=Tpg.

Such dependence we view in many phase thansitions (Peierls instability for example, where dielectric gap opens in some direction). But the order parameter for PG in cuprates is not Peierls instability, though i think it is connected with the lattice as a whole and the number of electrons in the zone.

We know Lenin's philosophical prediction that the electron is as inexhaustible as the atom.
And we may say that Bragg's peaks in metals also are as inexhaustible as electron.

I don't think we know all about Bragg reflections and minimizing total energy in such reflections in solid. Physicists don't like theorems of uniqueness of solution. So when they already know one solution, they become very angry at the one who search for other solutions. Why do we must continue search, if we already have the "right" solution?

PS. It is interesting. Braggs reflections ARE COHERENT, so we don't be puzzled that Bragged electrons can be, in principle COHERENT. And they must not be obligatory be in the single Bloch state. I can ask: is it possible for one electron be in the superposition of TWO Bloch's states with a lower energy, than electron in ONE Bloch state?

No problem.

 

[M@2]

The next Nature reference about 8 SC petals and 4 Pseudogap petals on 3d plot:
From the following article:
Competition between the pseudogap and superconductivity in the high-Tc copper oxides
Takeshi Kondo, Rustem Khasanov, Tsunehiro Takeuchi, Jörg Schmalian & Adam Kaminski
Nature 457, 296-300(15 January 2009)
http://www.nature.com/nature/journal/v457/n7227/fig_tab/nature07644_F3.html

We see broad red line with the name "Effective superconducting Fermi surface". This red line is the zone of two superconducting petals.
Black dotted line is the zone of two one half pseudogap petals.

Their difference: in PG zone of angles sample is dielectric, so it has no Fermi surface and dielectric (insulator) can't be metal and can't be superconducting.
In SC zone of angles sample is metal, so it can be superconducting. And MORE: at the beginning of SC zone electrons are more holes, than in closer directions to nodal direction, and empirical Chapnik rule predicts, at the beginning of SC zone of angles there be the highest SC gap.

More informative is figure 3 in this article. a), b), c)

 

[ZapperZ]

I used to do ARPES experiment on cuprates, or more specifically on the BSCCO family. So what are you trying to "teach" me here?

How is what you're saying tied to the original topic of this forum, which I'm guessing, you've long forgotten.

Zz.

 

[M@2]

How is what you're saying tied to the original topic of this forum, which I'm guessing, you've long forgotten.

ZapperZ, You can see my first post in this thread, post #4.

It is one of the main puzzles in the theory of superconductivity. But it is true as experimental fact.

We may also ask why gold and copper are not HIGH temperature superconductors?

I wanted to know, who can answer my question in red color

any theory is good only if it is simple enough to be understood by a barmaid.

Unfortunately it is not the case of gold and copper.

PS. Excuse, ZapperZ, but i never teach anybody, except when somebody ask advice directly.
In this thread i discuss results of published papers and post my own opinion.
Do You suppose, that i must post opinions of somebody else?

I used to be responsible for my own words, but not for words of other people.

 

[ZapperZ]

ZapperZ, You can see my first post in this thread, post #4.

I wanted to know, who can answer my question in red color

The phonon modes are not there, and there's no other mechanism that we know of in these material that can mediate the electron pairings.

Now, do you think a barmaid can understand that?

BTW, try the explanations you've given in this thread on any barmaid and see if she can understand those. If you can't do it, then don't impose that criteria on others.

Zz.

 

[M@2]

The phonon modes are not there, and there's no other mechanism that we know of in these material that can mediate the electron pairings.
Now, do you think a barmaid can understand that?

Even i don't understand such explanation. Though i had graduated from the best university of the USSR (my alumnies are Lev Landau, V Fock, Gamov, 4 rulers of Russia Lenin, Kerensky, Putin, Medvedev and about of 10 Nobel Prize winners), and my speciality was theoretical physics and specialization quantum mechanics. Even i don't understand SUCH explanation.

May be i must to be a barman?

Is such explanation published in peer reviewed journal or at least in a book?

By the way, barmaid quote was of discoverer of nucleus of atom. Krokodile Rutherford is worth of giving advice.

I'll don't discuss your explanation now. Let it be as it is. We can discuss it next year.

 

[M@2]

Is There Glue in Cuprate Superconductors?
Philip W. Anderson
Science 22 June 2007: 1705-1707.
Response to D. J. Scalapino’s E-Letter
http://www.sciencemag.org/content/316/5832/1705/reply

But let me reemphasize that these are quibbles about exactly how the fundamental interactions, identified 20 years ago, carry out their job; yes, much further work is needed, both experimental and theoretical, but not for sniffing out some mysterious glue.

Rereemphasized by M@2.

 

[ZapperZ]

Is There Glue in Cuprate Superconductors?
Philip W. Anderson
Science 22 June 2007: 1705-1707.
Response to D. J. Scalapino’s E-Letter
http://www.sciencemag.org/content/316/5832/1705/reply
Rereemphasized by M@2.

What does this have anything to do with this thread, which asked about METALS? The cuprates are not "metals". The phonon picture for metal superconductors is well-described.

And yes, I am fully aware of Anderson's RVB theory. I've even chatted with him about it. And for your information, Anderson was also one of those who predicted that superconductivity cannot go beyond 25K before the discovery of the cuprates, a fact that Robert Laughlin never failed to bring up.

You're citing him as if he's a religious prophet.

Zz.

 

[MTd2]

Let me try to understand. 4 petals = d orbital, 8 petals = f orbital.