Why some metals are not superconductors?

[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.

 

[M@2]

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.

Anderson asked important question about GLUE.
If scientists for a 25 years searched for GLUE and found nothing about origin of HTSC, may be it is worth for NSF to fund the NONGLUE direction a little bit?

Let me give example without GLUE. Quantum mechanics for many electron system (solid and atom for example) try solve Schroedinger equation for one electron in the averaged field of other electrons and AFTER SOLVING put electrons on calculated quantum levels.

This method IS very successful.
Let us we have initially two ORBITALS for ONE electron with the collinear wavevectors in opposite direction near Fermi surface:
psi_1(p1), psi_2(p2), |p1-p2|=2*p_F (exactly!)

There may be ORDER PAPAMETER interaction (matrix element, connecting those two orbitals) of some origin (Bragg reflections, phonon mode, CDW, SDW,...). Elementary quantum mechanics says there must be repellion of levels and there must be a gap at Fermi level.

For lower level at Fermi level unnormalized wave function:
PSI=psi_1(pF)+psi_2(-pF)

If we switch on magnetic field, find optimal PSI in magnetic field and calculate current of optimal PSI we get microscopic London equation for one superconducting electron with doubled coefficient before vector potential:
J=2*const*A

Doubled becouse eA/m for both initial orbitals have the same value (p₁ an p₂ have opposite direction).

So we have gap, we have half flux quantization. And we don't need glue.

I don't want to debate, what is true in HTSC. I only give example, that it shouldn't to ignore nonglue (nonpairing) variants from the beginning.

 

[ZapperZ]

Anderson asked important question about GLUE.
If scientists for a 25 years searched for GLUE and found nothing about origin of HTSC, may be it is worth for NSF to fund the NONGLUE direction a little bit?

Let me give example without GLUE. Quantum mechanics for many electron system (solid and atom for example) try solve Schroedinger equation for one electron in the averaged field of other electrons and AFTER SOLVING put electrons on calculated quantum levels.

This method IS very successful.
Let us we have initially two ORBITALS for ONE electron with the collinear wavevectors in opposite direction near Fermi surface:
psi_1(p1), psi_2(p2), |p1-p2|=2*p_F (exactly!)

There may be ORDER PAPAMETER interaction (matrix element, connecting those two orbitals) of some origin (Bragg reflections, phonon mode, CDW, SDW,...). Elementary quantum mechanics says there must be repellion of levels and there must be a gap at Fermi level.

For lower level at Fermi level unnormalized wave function:
PSI=psi_1(pF)+psi_2(-pF)

If we switch on magnetic field, find optimal PSI in magnetic field and calculate current of optimal PSI we get microscopic London equation for one superconducting electron with doubled coefficient before vector potential:
J=2*const*A

Doubled becouse eA/m for both initial orbitals have the same value (p₁ an p₂ have opposite direction).

So we have gap, we have half flux quantization. And we don't need glue.

I don't want to debate, what is true in HTSC. I only give example, that it shouldn't to ignore nonglue (nonpairing) variants from the beginning.

This is puzzling. It's as if Landau's Fermi Liquid theory isn't used already!

And the "non-glue" scenario IS being considered. Anderson's RVB theory has NOT been ignored at all!

This is utterly irrelevant to the original question in this thread. This thread is done.

Zz.