# Why some metals are not superconductors?

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

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.

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 dont 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 cant 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.

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

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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.

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 cant 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
Gold Member
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).

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 TDebye 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.

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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.

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

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

Who sais so?

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.

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.

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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.

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

Zz.

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 beleive 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?

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f95toli
Gold Member
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.

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 omegaDebye? 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).

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ZapperZ
Staff Emeritus
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 omegaDebye? 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
Homework Helper
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 omegaDebye? 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.