Simplicity will out: Novel experiment-based expression explains behavior of unconventional superconductors

December 29, 2014 by Stuart Mason Dambrot, Phys.org feature
A phase diagram for heavy-electron superconductors. In region I, only itinerant heavy electrons exist below TL owing to complete hybridization of the f-moments with background conduction electrons; in region II, collective hybridization is not complete so that heavy electrons coexist with partially hybridized local moments; in region III, these residual moments order antiferromagnetically (AF) at TN and the surviving heavy electrons become superconducting (SC) at a lower temperature, Tc. The coupling of heavy electrons to the magnetic spin fluctuations emanating from the QCP is responsible for the superconductivity in all regions. Credit: Yang Y-F, Pines D (2014) Emergence of superconductivity in heavy-electron materials. Proc Natl Acad Sci USA 111(51):E18178-18182.

(Phys.org)—Superconductivity – perhaps the leading example of emergent quantum behavior in matter – was discovered in 1911 but lacked theoretical explanation for almost five decades. In 1957, John Bardeen, Leon Cooper, and John Robert Schrieffer (BCS) developed a microscopic theory of superconductivity1 that came to be known as the BCS theory, which describes superconductivity as a microscopic effect caused by a condensation of Cooper pairs into a boson-like state. BCS theory explains the behavior of what are now known as conventional superconductors – metals for which phonons provide the recently controversial "pairing glue" that leads to the effective attractive quasiparticle interaction responsible for their superconductivity. (Phonons are quantized lattice vibrations, and quasiparticles are mobile electrons or holes in materials; both are quantized elementary excitations.)

As it is wont to do, history is now repeating itself: Unconventional superconductors, in which pairing glue and pairing condensate symmetry differ from conventional superconductors, were discovered in the 1980s – but while it appears from both theory and experiment that electronic spin fluctuations provide the pairing glue for the unconventional , a general model remains elusive. Recently, however, scientists at Chinese Academy of Sciences, Beijing and the Santa Fe Institute proposed such a model in the form of an experiment-based phenomenological BCS-like expression for the superconducting transition temperature Tc in heavy-electron materials that is based on a simple model for the effective range and strength of the spin-fluctuation-induced quasiparticle interaction, and reflects the unusual properties of the heavy-electron normal state – in which electrons gain mass as local electron spins lose their magnetism – from which superconductivity emerges.

Prof. David Pines discussed the paper that he and Dr. Yi-feng Yang published in Proceedings of the National Academy of Sciences. (Pines and Yang began collaborating in 2007 and have since written nine papers together, with Pines acting as the spokesman for their collaboration.) "The basic challenge we faced was that of exploring new territory – that is, to see whether we could make spin-fluctuation-induced superconductivity more accessible by developing, at a phenomenological level, BCS-like expression for unconventional superconductors that was based on a spin-fluctuation mechanism for their superconductivity," Pines tells Phys.org. (In science, phenomenology describes knowledge based on empirical observations of phenomena that is consistent with, but not derived from, theory.) Pines adds that the scientists decided to start with heavy electron superconductors because these are exceptionally pure; their unusual normal state behavior and how Tc varies with pressure have been studied detail; and, unlike the cuprates, there is a general consensus that antiferromagnetic spin-fluctuations provide the pairing glue for their superconductivity.

The scientists faced several challenges in using a simple model of the effective range and strength of the spin-fluctuation-induced quasiparticle interaction and reflects the unusual properties of the heavy-electron normal state from which superconductivity emerges to develop a BCS-like equation for Tc in heavy-electron materials, the first being providing a quantitative explanation of the measured pressure-induced variation in Tc in the heavy-fermion superconducting so-called "hydrogen atoms" of – cerium-cobalt-indium 5 (CeCoIn5) and cerium-rhodium-indium 5 (CeRhIn5). "Explaining that variation is a significant measure of the success of any proposed model of their superconductivity, so we were delighted to find that we could provide the explanation of that variation by further specifying that for a given material, the range of energies over which a quantum critical spin-fluctuation induced interaction will be attractive must be proportional to its coherence temperature, T*, at the pressure pL, at which Tc is maximum."

Comparison of theory and experiment for the ordering temperatures measured in CeCo(In1−xCdx)5 and CeRhIn5. (A) Pressure variation of the predicted dimensionless pairing strength (Methods), κ(p) = kBT*(p)NF(p,Tc). (B) Scaling of ln(Tc/T*m) and κ(p)−1 (scaled) for CeCoIn5 and CeRhIn5. (Inset) The experimental values of T*(p) that are used to obtain κ(p) in both compounds (7, 19). (C) Comparison of the predicted (solid lines) and experimental Tc and TN in CeCo(In1−xCdx)5 and CeCoIn5 with η = 1.30 and λmax = 0.62 (19, 21). (D) Comparison of the predicted (solid lines) and experimental Tc and TN in CeRhIn5 with η = 3.09 and λmax = 1.23 (18). Credit: Yang Y-F, Pines D (2014) Emergence of superconductivity in heavy-electron materials. Proc Natl Acad Sci USA 111(51):E18178-18182.

Secondly, their model predicts a similar pressure variation for other heavy-electron quantum critical superconductors. "A good model or theory not only explains past measurements, but has predictive capabilities," Pines points out. "Therefore, a key further test of our BCS-like expression is its prediction that a measurement of the variation of Tc with pressure in additional heavy electron materials will show a dome-like structure, with the maximum in Tc occurring at the pressure at which localization sets in."

A crucial further test, Pines continues, was that the model quantifies their variations in Tc with a single parameter. "Once one fixes, at a given pressure, the material-sensitive parameter that measures the relative effectiveness of the attractive spin-fluctuation induced interaction in bringing about superconductivity, then there are no free parameters left in our BCS-like expression for the superconducting transition temperature at other pressures."

To address these challenges, Pines notes that the two-fluid model that yields correct specific heat results for a number of heavy-electron compounds was central to understanding both the unusual normal state properties of heavy electrons3, as well as their superconductivity. "The two-fluid model provides a simple and successful phenomenological model for the emergence of heavy electron behavior at T*, including the magnitude and logarithmic temperature variation of the specific heat produced by heavy electron density," Pines explains. "It also led to the discovery of universal scaling behavior with T*, while careful measurements of the single ion Kondo effect showed that the physical origin of T* is the interaction between the nearest neighbor local moments whose collective hybridization with the background conduction electrons leads to the emergence of heavy electron behavior in the normal state." (The Kondo effect describes the scattering of conduction electrons by single magnetic impurities in a metal, resulting in a characteristic change in electrical resistivity with temperature.)

The scientists determined that in the case of CeCoIn5, the range of the effective attractive interaction found in microscopic strong coupling calculations is remarkably close to what they proposed phenomenologically. "Making this comparison is a very important check on our phenomenology," Pines says. "In carrying it out, we extrapolated the results from a study of microscopic strong coupling calculations of spin-fluctuation-induced superconductivity in the cuprates4, where it was found that a BCS-like expression could parameterize their numerical results quite well, to heavy electrons."

Pines says that the question of whether their phenomenological approach can be extended to the cuprates and any other in which scaling behavior for the spin-lattice relaxation rate with Tc has been seen at or near optimal doping levels "is a very interesting and important question, and one we are currently trying to answer. For the cuprates, one can be guided by the strong coupling microscopic calculations and nuclear magnetic resonance (NMR) experiments that enable one to determine the range of the attractive interaction at optimal doping." (In NMR, nuclei in a magnetic field absorb and re-emit electromagnetic radiation.) "What's less clear is the doping dependence of the density of states and the coupling strength g, which together will fix the dome structure seen experimentally. We find we can choose these in such a way as to yield this structure, but would like to be able to relate that straightforward phenomenology to experiments on the magnetic properties in the normal state. That is a work in progress."

Currently, Pines tells Phys.org, the scientists are working on two projects: extending to the cuprates their phenomenological approach to quantum critical spin-fluctuation-induced superconductivity in heavy-electron materials, and – in further collaboration with Gilbert Lonzarich5,6,7 at Cambridge University – writing a perspective on basic concepts in heavy electron physics exploring why it has proven so difficult to develop a microscopic theory of the emergence and subsequent behavior of heavy electrons in Kondo lattice materials."

"Our successful phenomenological approach to emergent behavior in heavy electron materials can serve as a guide to developing a microscopic theory of that behavior," Pines concludes. "It also provides an example of how to deal with the challenging problems posed by the emergent behavior found in other strongly correlated electron materials: First, use experiment as a guide to develop a consistent phenomenological model that incorporates the organizing principles that might be responsible for that behavior; second, then and only then, try to devise and solve a simple microscopic model that incorporates these organizing principles and provides results that can be compared with experiment."

Explore further: Electron spin could be the key to high-temperature superconductivity

More information: Emergence of superconductivity in heavy-electron materials, Proceedings of the National Academy of Sciences 111:51 18178-18182 (2014), doi:10.1073/pnas.1422100112

Related:

1Microscopic Theory of Superconductivity, Physical Review 106:162 (1957), doi:10.1103/PhysRev.106.162

2Quantum critical behavior in heavy electron materials, Proceedings of the National Academy of Sciences 111:238398-8403 (2014), doi:10.1073/pnas.1407561111

3Scaling the Kondo lattice, Nature 454:611-613 (2008), doi:10.1038/nature07157

4Spin-fluctuation-induced superconductivity in the copper oxides: A strong coupling calculation, Physical Review Letters 69(6):961–964(1992), doi:10.1103/PhysRevLett.69.961 [Erratum: Physical Review Letters (1993) 71:208, doi:10.1103/PhysRevLett.71.208]

5Superconductivity without phonons, Nature 450:1177-1183 (2007), doi:10.1038/nature06480

6Magnetically mediated superconductivity in quasi-two and three dimensions, Physical Review B 63:054529 (2001), doi:10.1103/PhysRevB.63.054529

7Magnetically mediated superconductivity: Crossover from cubic to tetragonal lattice, Physical Review B 66:224504 (2002), doi:10.1103/PhysRevB.66.224504

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Wake
5 / 5 (2) Dec 29, 2014
And to think that Professor Pines is the spokesman. Next time let's get Dr. Yi-feng Yang to explain it in Chinese. I'm sure that would be a LOT clearer to Americans.
johanfprins
Dec 30, 2014
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McIek
Dec 30, 2014
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McIek
Dec 30, 2014
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McIek
Dec 30, 2014
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johanfprins
Dec 30, 2014
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smd
5 / 5 (1) Dec 30, 2014
All the theories on superconduction are consistently BS models

Please expand on your rather heavy-handed judgement - that is, tell us why you think this is the case.
johanfprins
1 / 5 (1) Dec 30, 2014
@ smd
All the theories on superconduction are consistently BS models

Please expand on your rather heavy-handed judgement - that is, tell us why you think this is the case.
Since a Cooper-pair is a senseless mathematical concoction which cannot exist (therefore no "C"):

But even if pair-formation is possible by any mechanism, it is not required for superconduction to occur. The charge-carriers are localised Mott-type stationary states which start to move by means of quantum fluctuations when charge-carriers are injected into this phase. To do this they need not have integer spin. In fact it is even possible that they can form a ferromagnetic-array of localised orbitals. This is explained in detail in:

https://www.resea...=prf_pub
McIek
Dec 30, 2014
This comment has been removed by a moderator.
johanfprins
1 / 5 (1) Dec 30, 2014
@ Mclek=Zephyr,

I do not see any Cooper Pairs in this pathetic picture! Cooper pairs are alwys MOVING in order to cause phonons: What is moving in this picture? Duck-farts that we cannot see?

All I see are regular arrays of STATIONARY localised states!
McIek
Dec 30, 2014
This comment has been removed by a moderator.
johanfprins
3 / 5 (2) Dec 30, 2014
@ Mclek=Zephyr,

How long was the exposure? Stop being such a liar!!! At what speed are your duck-fart "ripples" moving? One a day?

You are still too stupid to understand what I have proposed and proved mathematically about waves. Try reading real physics and to understand my manuscripts.

BTW: Thre are NO charge-waves within a superconductor.
McIek
Dec 30, 2014
This comment has been removed by a moderator.
smd
5 / 5 (1) Dec 30, 2014
All the theories on superconduction are consistently BS models

Please expand on your rather heavy-handed judgement - that is, tell us why you think this is the case.

a Cooper-pair is a senseless mathematical concoction which cannot exist

Why can't Cooper pairs exist?
How much of current particle physics and quantum theory do you think is "mathematical concoction"?
johanfprins
1 / 5 (1) Dec 31, 2014
Why can't Cooper pairs exist?
How much of current particle physics and quantum theory do you think is "mathematical concoction"?

All of it, since all of it is based on the concept of "time-dilation" and "space-time". Both concepts are absurdly impossible. Physics is not absurd: See: https://www.resea...=prf_pub

Schroedinger's equation is not a concoction since it is consistent with Maxwell's equations. The Copenhagen interpretation is not just a concoction, but unadulterated Voodoo.
smd
5 / 5 (1) Dec 31, 2014
How much of current particle physics and quantum theory do you think is "mathematical concoction"?

All of it, since all of it is based on the concept of "time-dilation" and "space-time". Both concepts are absurdly impossible.

Schroedinger's equation is not a concoction since it is consistent with Maxwell's equations. The Copenhagen interpretation is not just a concoction, but unadulterated Voodoo.

Thank you for sharing, but...Yikes! All of it? Understand that (1) mathematics is a language that is highly precise and can be implemented in experimentation to test hypotheses regarding a given theory (the scientific method); (2) that as a language it is inherently metaphorical and so may have predictive value without being structurally accurate (e.g., Ptolemaic cosmology); and (3) as physics progresses, earlier theories and concepts are shown to be either wrong or subsets (think Newton and Einstein).

Sadly, I doubt that this will lead to a productive conversation.
johanfprins
Dec 31, 2014
This comment has been removed by a moderator.
smd
4.3 / 5 (6) Jan 01, 2015
You have previously argued this point on this forum and others. Either way, your language is unwelcome. Please take your vitriol elsewhere.
johanfprins
Jan 01, 2015
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McIek
Jan 01, 2015
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johanfprins
Jan 01, 2015
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Captain Stumpy
5 / 5 (2) Jan 01, 2015
Nobody who has ever engaged me in terms of the rules of physics has ever experienced vitriol from me
@PrinsTROLL
this is a blatant lie and it can be proven right here on PO alone
especially with regard to discussion of physics with thefurlong
Look at any of the following links for proof of your hostility to anyone promoting an idea YOU don't like
http://phys.org/n...rse.html
http://phys.org/n...pet.html
http://phys.org/n...ity.html

your "version" of no vitriol while engaging in the terms of the rules of physics has included such lighthearted banter like
Shitfur
Shitlong
your insane meanderings
a criminal hiding behind anonymity
enjoy yourself shithead!
any amount of training can ever replace the shit in your head with any brains!
arrogant little arsehole
YOU obviously do not know who your mother and father are
You are... bastard son of a whore
so save your BS
Captain Stumpy
5 / 5 (2) Jan 01, 2015
@prins
whereas i might actually agree with some of your comments about ZEPHIR, your post of the following
I am not frustrated with my physics but with arseholes like YOU and the editors of mainstream physics journals who are tooo stupid to argue REAL: physics!!
is nothing more than a demonstration of your conspiratorial outlook and the need for you to blame others for your own shortcomings

you cannot get published because you are not given them reputable science or you are supporting fringe crackpot ideas, REGARDLESS of your prior publications or legitimate research

In essence, you are angry about not being published because they caught you being a pseudoscientist and called you on it

you have an options at this point. you can:
- change and go back to legitimate science
-continue with your pseudoscience and continue to be ignored/refused by legitimate journals

this is NOT a failing of the peer review system
it is PROOF that it works as it should!
johanfprins
Jan 01, 2015
This comment has been removed by a moderator.
Captain Stumpy
5 / 5 (2) Jan 01, 2015
If you want to make such allegations, one expects that, a sane person with integrity (which you have proved over and over an over again on this forum you are not) will back it up with examples from my publications which have been refused, and which are all available on the internet.
@prinsTROLL
but johannie... you've provided those YOURSELF
these can be found amongst your delirious denigrations among those links above that i posted
Simply search for your own name!

I will give the links again, since i know your age and nature might prohibit you from actually backing up or re-reading anything that is not complimentary to you

http://phys.org/n...rse.html
http://phys.org/n...pet.html
http://phys.org/n...ity.html

you cannot get me angry with your
bastard scumbag
or anything else
i've studied you
I've seen your worst
LMFAO

P.S. Pimp Dad's means no bastard, BTW
LOL
Captain Stumpy
5 / 5 (2) Jan 01, 2015
@prins [cont'd]
make such allegations
i've stated NO allegations
i've stated facts borne out by your own words posted to the above links
a sane person with integrity (which ...you are not)
and you consider your posts and hostility the epitome of sanity and integrity?
you are the one claiming a mass conspiracy without any evidence
homourable!
[sic]
it's actually spelled "honourable" (using the Brit spelling)
or "honorable" using the US spelling
no need for any "m" in there

the rest of that post was simply prins lashing out because I hit a sore spot with his ego and it hurts that it cannot be refuted

and before you go there, jp
publishing a book is not the same thing as publishing a peer reviewed paper
NOR is it the same if you get published to one of those crackpot sites that will support even ZEPHIR's aw/daw or cd's electric craters/grand canyon eu

that is what is called "pseudoscience"

just because you ONCE were legit
doesn't mean you still are
OZGuy
5 / 5 (2) Jan 01, 2015
JP
A quick heads-up... you are NOT Galileo, stop referencing him as though your personal bedevilments elevates you to his historical stature.
del2
5 / 5 (5) Jan 01, 2015
@prins
I downloaded your paper referenced by you above.
A brief response (because space is limited here):
Einstein said that Maxwell's laws should be valid in any Inertial Reference Frame.
From this is deduced that the speed of light must be the same in any IRF.
From this is deduced that there is no absolute time.
You state as an a priori assumption that there is absolute time, that it is sufficient that you say so, and that anyone who disagrees with you is an idiot.
Is that an accurate summary?
imido
Jan 01, 2015
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