Monday, August 03, 2009

Röser's equation, again

Over the weekend, I thought again about Röser's equation relating the transition temperature of high-temperature superconductors to a characteristic length scale called "doping distance". Having reread the Proceedings paper where it is described, I wanted to add a few comments to our last week's post, only to realize that blogger has a restriction to the length of a comment. So, here is a second post.

Let me just repeat the main point of the "Röser formula":

It claims a simple linear relation between the inverse of the superconducting transition temperature of a wide range of superconducting materials, and a so-called "doping distance". This relation is shown in the following plot:

(from: A Correlation Between Tc of Fe-based HT Superconductors and the Crystal Super Lattice Constants of the Doping Element Positions by Felix Huber, Hans Peter Roeser, Maria von Schoenermark, Proc. Int. Symp. Fe-Pnictide Superconductors, J. Phys. Soc. Jpn. 77 (2008) Suppl. C, pp. 142-144)

Here are a few more thoughts of mine about this relation.

Thermal de Broglie wavelength

Using the standard definition of the thermal de Broglie wavelength for a Cooper pair of two electrons with free masses, the Röser equation

4 π k me(2 x)2 n−2/3 = h2/ Tc

actually boils down to

(2 x) × n−1/3 = λc

where λc is the thermal de Broglie wavelength of the Cooper pair at the critical temperature Tc, where superconductivity breaks down.

In the proceedings paper, n = 1, so the factor n−1/3 can be dropped. Moreover, it is said to take values of n = 2 or 3 for other superconductors with a layer structure, depending on the number of layers in the unit cell. It's not completely clear to me how it is motivated.

Substances Covered

In the proceedings paper, the authors discuss doped iron arsenides LO(1−Δ)F(Δ)FeAs, where L is a rare earth, L = La (Lanthanum), Gd (Gadolinium), Ce (Cerium), Pr (Praseodymium), Nd (Neodymium) or Sm (Samarium) - see table 1 of the paper. These materials are labeled as "LOFFA", "GOFFA", "COFFA", "POFFA", "NOFFA", and "SOFFA" in the plot.

The other data points in the plot refer to cuprate superconductors - the substances labeled ...CO, or Bi-2212, where the numbers denote the composition. These cuprates are discussed in several Acta Astronautica papers, for example Acta Astronautica 65 (2009) 489, which unfortunately I do not have access to.


In the examples of the rare earth iron pnictides, superconductivity can be reached by replacing, in an ideal LOFeAs lattice, some of the oxygen atoms by fluorine atoms. Depending of the amount of fluorine, the critical temperature for superconductivity can take different values. The Physics article on High-temperature superconductivity in the iron pnictides shows phase diagrams for "LOFFA" and "COFFA".

In "COFFA", CeO(1−x)F(x)FeAs, for example, superconductivity sets in only when at least 6 percent of the oxygen atoms are replaced by fluorine, and the transition temperature is highest for a replacement of about 16 percent of the oxygen atoms by fluorine:

(from: Structural and magnetic phase diagram of CeFeAsO(1-x)F(x) and its relationship to high-temperature superconductivity, by Jun Zhao et al., arXiv:0806.2528v1, and Nature Materials 7 (2008) 953-959.)

The percentage of replaced atoms is called the "doping", and it is usually denoted with x, which should not be confused with the "doping distance" in the Röser paper. In the formula above for the substances, I have denoted doping with Δ, as in the Röser paper.

The "doping distance" x

The Röser formula compares the thermal de Broglie wavelength of a Cooper pair at the superconducting transition temperature with a "doping distance" x and states that they are equal, up to a geometry factor. The crucial point, then, is how to arrive at the "doping distance".

In the proceedings paper about iron arsenides, it is argued that every two of the "doping" fluorine atoms group around one iron atom, and that these "decorated" iron atoms form, again, a regular lattice. Such a lattice is usually called a superstructure.

In the example of "COFFA" at the "optimal" doping of Δ = 0.16, this reasoning implies that 8 percent of the iron atoms are neighbored by two fluorine atoms each, and the superstructure of the decorated iron atoms has to comprise 1/0.08 = 12.5 standard unit cells. They argue that this means that 5 unit cells are put on top of each other, yielding a doping distance of 5 times the height c of the unit cell, or x = 5 c.

For the other doped lanthanide iron arsenides, a similar reasoning is used. The constructions of the superstructure and the resulting doping distances are documented in table 1 of the proceedings paper.

Open questions

To me, construction of the "doping distance" is not really comprehensible, and it seems that there are a few points where the paper just glosses over:

I am not sure whether (1) the dopant fluorine atoms group pairwise at iron atoms and (2) if the decorated iron atoms indeed form a superlattice. However, this may be checked experimentally. But then, (3), if there is a superlattice, it is not clear to me why it should be ordered in the way claimed in the paper, with a pattern stacking five unit cells on top of each other for "COFFA", for example. There can be many ways to arrange unit cells to form a superlattice with the right supercell volume. This is more obvious in the case of "LOFFA", where the supercell comprises 18 unit cells, and there seems to be no a priori reason to select a superstructure which has 6 unit cells stacked on top of each other.

In other words, the determination of the "doping distance" involves an arbitrariness which may be used to select x in a way to fit the formula, and there is no real discussion of the selection rules in the paper. This arbitrariness, however, could be resolved by experiments which actually measure the superstructure.

There is another point which puzzles me about the paper, which is the application of the formula to the cases of "optimal doping" only, i.e. those values of doping where the transition temperature for the substance at hand is maximal.

I don't see a good reason why the formula should not apply at any value of doping, if there is a relation between the transition temperature and the "doping distance". Then, however, there is the problem that around the maximum, different values of doping give the same transition temperature, hence should have the same doping distance. This can be seen very nicely in the phase diagram of "COFFA" above. Maybe this point can be arranged for somehow, and maybe it is discussed in the Acta Astronautica papers.


Thinking about it, while the Röser relation is indeed amazing, it's unclear to me how much of an "a posteriori" selection bias concerning the "doping distance" goes into it.

However, as the relation makes strong claims about the arrangement of the dopant atoms, this probably can be checked experimentally.

If it comes out that the relation indeed holds, it will be exciting to understand what it means for the physics of superconductivity.


  1. It will be interesting to see where this goes.

  2. In my understanding repulsive force of electrons near holes must remain compensated by neighboring atoms (whose attractive forces are keeping whole lattice together like rivets) in as regular way, as possible. This puts rather strict limit into arrangement of neighboring atoms around holes.

  3. Dear Stefan:

    Forget for a moment the plausibility of this equation, and imagine it to be true. What does it say about the necessary structure for a 300K superconductor?


  4. Hi Stefan,

    I think it is an issue of some symmetry or asymmetry within the cuprates, see arXiv.


  5. Arun asked:
    "What does it say about the necessary structure for a 300K superconductor?"

    Maybe it says, there is no such
    sperconductor, because that would
    afford a doping distance shorter than
    any reasonable distance in a crystal. :=(

  6. Nice to see such application to understand the characteristics.

    It's the best we can do to theoretically bind what is happening in the universe in relation to QGP and see time travel scenario's that break the rule of thumb? Energy traveling quite freely as to what is the cosmic relation? Ummmm... wild thoughts for sure.

    So the Japanese group set about doping its material—adding a sprinkling of foreign atoms to the recipe—to try to raise the transition temperature. Replacing some of the oxygen atoms with fluorines brought on superconductivity at 7 K. Swapping arsenic for phosphorus resulted in superconduction up to 26 K, a temperature high enough to get physicists’ attention all around the world and to spark a flurry of research when the group’s arsenic paper appeared in late February 2008. By the end of March, groups in China had similar compounds superconducting just above 40 K. A month later, 56 K.See:An Iron Key to High-Temperature Superconductivity?


  7. Imagine such a place that determines a beginning for all expression of that is remembered and held as information so as to develop what structure now begins as the standard model shall make this table as such, from it's mapped capabilities?

    Just dreaming.:)

  8. Dear Arun, Georg,

    the situation at room temperature is not that hopeless, because of the square root of temperature in the thermal de Broglie wavelength.

    For simplicity, take LaO(1-d)F(d)FeAs, or "LOFFA", from the table 1 they provide in the paper. It has a unit cell height of 0.9 nm (it's aboout the same for the other rare earth iron arsenides), and with a transition temperature of 25.5 Kelvin, they claim a doping distance of 5.22 nm.

    Now, if we multiply temperature by 16 = 4², we are safely above room temperature. To reach such a transition temperature, the "doping distance" has to shrink by a factor 4, hence reduce to 1.3 nm, which is about 1.5 times the unit cell height.

    So, a doping ratio of about 2/3 could be sufficient, and at least according to the Roesler formula applied to rare earth iron arsenides, this could yield superconductivity at the boiling point of water ;-).

    Cheers, Stefan

  9. /*..what does it say about the necessary structure for a 300K superconductor? ... Maybe it says, there is no such sperconductor, because that would afford a doping distance shorter than any reasonable distance in a crystal....*/

    Nope, as doping distance isn't equivalent of lattice constant here and we can increase Tc by increasing of periodicity parameter n, too. In illustrative way, if we create a hole stripe across every two or three elementary cells in lattice, we can achieve a lower current limit in bulk, but higher Tc. Of course such way of doping requires advanced solid-state engineering.

  10. Please note, that the HT superconductors with highest Tc achieved are quasicrystals as they're composed of many components in similar way, like metal glass. This reduces doping distance by increase of lattice constant under decrease of current limit at the price.

  11. Zephir,

    quasicrystals as superconductors with the highest known transition temperature? Frankly, I don't believe a word. Could you please be a bit more specific and provide a reference? Or do you just mean the layered- structure ceramic cuprate superconductors?

    Thanks, Stefan

  12. All HT superconductors known so far are layered. Critical temperature depends upon the number of copper-and-oxygen layers per block - the more of these layers, the higher the critical temperature. For example material with critical temperature of -148 degrees C has three consecutive layers made of copper and oxygen and atoms in each block. The incorporation of another metals into oxide layer has the only purpose: to decrease periodicity of lattice and to increase number of atoms, which are compensating be their attractive forces the pressure of electrons in hole stripes.

  13. /* frankly, I don't believe a word... */
    My question is, if you understood the concept? If not, it's irrelevant for me, if you're believing in it, or not. Belief or disbelief (i.e. belief into negation) has no place in science and it's completely irrelevant to dialectic discussion. And if you haven't understood concept, it has no meaning to ask for another evidence and to demonstrate in such way, your acceptation of new ideas is completely belief based.

  14. Hi Stefan,

    Thanks for dissecting and distilling this paper down a little further. If anything it confirms that the confusion I had in my first reading of it isn’t restricted to me only not having the tool set required to consider it properly, as you pointed out some of the ambiguities I initially had noticed. This is one time where I wished one of the authors would drop by as has happened a few times here in the past.

    One thing this has prompted me to do is to look a little deeper into this whole high temperature superconductivity issue and have found it is riddled with a general lack of fundamental understanding and with it plenty of controversy. One of these is that the onset of super conductivity and where the magnetic properties of such substances set in may not be the same thermal point, with in some instances the magnetic ones not appearing at all. This has some to wonder if these are even related properties of such substances.

    For me at this point this all suggests that with superconductivity at high temperature we are more at an alchemist’s stage, rather than a sounder scientific one, for result appear to be racing far ahead of theoretical explanation. To some degree this is all reminiscent of that time when many were trying to turn lead into gold, only in this case they have managed it (so to speak) and although they can tell you how, still have no clear idea what it was that they did which accomplished it. This formula of Roser suggests one of the hows, yet still not how this is consistent with any known theory. Then again like you said this is the true value of science, for who knows where a better understanding of this could lead.



  15. Thank heavens, my dreams of room-temperature superconductors and of winning the lottery - both remain alive! :) :)

  16. Hello Stefan,
    thank You for "dissipating" my
    guessing, guided by pessimism.
    What do You think about publishing
    this correlation in a rather specialized
    journal, which is unknown to most
    physicians, isn't it?

  17. Zephir: Stefan said he doesn't believe a word because you haven't provided a reference. Would you please omit the evasion and add facts or shut up. Thanks,


  18. /* this is consistent with any known theory..*/
    The question is, which theory or explanation mainstream community is willing to consider as a "known"...;-) But this is not my problem.

    Superconductivity (SC) is complex phenomena, AWT explanation is based on EM-EM interactions and it's relevant for highest temperature. As the temperature decreases, spin-spin and phonon interactions take place so that Collin Humphreys', BEC and BCS models becoming relevant gradually due the gradual degree of condensation (1D EM interaction >> 2D spin-EM coupling ~ 3D spin-spin interactions > 1D spin-phonon interactions). In addition, at the presence of paramagnetic atoms spin interaction and 3D models of SC are more preferred (oxypnictides). In thin layers SC gets degenerated into 1D and surface plasmons and/or Bloch waves are getting into game.

    So it's rather ineffective try to find a general superconductivity model without ab-initio calculations. From practical purposes only the simplest AWT model of HT superconductivity is relevant, because we are interested just about room temperature SC without additional effects - or not? Such mechanism requires nontrivial geometry though - so that theorists struggling with more complex models, which are more accessible experimentally.

  19. /*.. he doesn't believe a word because you haven't provided a reference..*/
    This is why physicists cannot accept new explanations, no matter how simple they're are - they're indeed "missing a reference". Such approach leads to blind development of ad-hoced formal regressions based on existing theories without deeper insight from more general perspective.

  20. Zephir: This is why physicists cannot accept new explanations, no matter how simple they're are -

    What we don't accept are NO explanations, and that's why Stefan asked for a reference. In any case, I suggest you keep your "deeper insight from more general perspective" to your own blog and focus on the topic of this post. Which is Röser's work. Thanks,


  21. OK, Bee... my very last few questions are

    1) did someone understand my explanation of HT superconductivity (i.e. can someone reproduce it by its own words)?
    2) If yes, do you personally consider such explanation difficult and/or ad-hoced?
    3) If not, can anyone explain, why such explanation wasn't proposed and checked before many years already?

    We are dealing with limits of so called "scientific method" by now.

  22. /*..we don't accept are NO explanations..*/
    Indeed. At first, please speak for yourself, at second, please feel free to prove, my explanation is NO explanation - and I'll shut up by your command.

    If you cannot prove it, you have NO explanation for your stance - so I can say easily, we are facing pathological skepticism, again. The refusal of some explanation isn't so free game, as you and other skeptics probably believe - it should be based on the predicate logic in the same way, like original explanation.

    The fact, you didn't understand my explanation is irrelevant, until you prove, my explanation is inconsistent with respect of predicate logics, i.e. it cannot be understood at all. Without it we could say, every explanation is BS.

  23. Hello Stefan, Bee,
    this "Zephir" seems to be a natural
    born Jesuit. I recommend You stop
    to try to "educate" him, just erase
    his posts, when they are off topic.

  24. LOL, I was censored and attempted to silence here already - so why I shouldn't consider Miss Bee a Jesuit instead of me? Even usage of "we" pronoun during presentation of personal opinion can be classified as an attempt for manipulation of readers - so I refused it assertively. Stop the demagogy and labelling of opponents - or I can feel like Galileo here easily...

    People become uncommunicative or even dismissive suddenly, when they met with some new idea from person, which isn't apparent authority, because they risking their social status. This is natural stance.

  25. IMO the problem of HT superconductivity understanding is mainly the matter of mechanisms, which prohibited mainstream science to consider simplest explanation from its very begining (in accordance to Occam's razor principle).

    It's not technical - but mostly social problem. I can demonstrate it on many other examples.

  26. Zephir:

    At first, please speak for yourself, at second, please feel free to prove, my explanation is NO explanation - and I'll shut up by your command.

    What exactly is your problem with me speaking for both my husband and me if he is at work and can't reply?

    LOL, I was censored and attempted to silence here already - so why I shouldn't consider Miss Bee a Jesuit instead of me?

    Exactly what have I allegedly "cencored"? Your comments are so far complete, but I am pretty close to deleting all of them since you are only contributing off-topic self-promotion that isn't useful neither for our readers nor us.

    If you cannot prove it, you have NO explanation for your stance

    The only "stance" I've tried to get across, Zephir, is that this is *not*, I repeat *not*, the place for you to promote your alternative explanations of something. Please do this elsewhere. If you're pissed off because I'm not interested in your great insights, fine. I could care less. I am also absolutely not interested in you complaints about the academic system.

    I hope that was clear. One more off-topic comment of yours and all your comments go out the window.



  27. /*..what exactly is your problem with me speaking for both my husband and me if he is at work and can't reply..*/
    Well, because it's a sort of manipulative behavior. It's well known, demagogic politicians like Stalin, Hitler etc. misused the "we" pronoun for manipulation of masses. It's nothing personal from my side, as I don't like manipulation in general - it prohibits us in seeing of things clearly.

    /*..Exactly what have I allegedly "cencored"? ..*/
    You wrote yesterday:

    "During the last weeks I've deleted several of your comments and another one in this comment section. Would you please keep..", etc..

    so I don't understand quite your question. Do you?

    /*...this is *not*, I repeat *not*, the place for you to promote your alternative explanations of something...*/
    I don't understand, why are you analyzing Roser equation in public just here, after then. In fact, every other comment would be off-topic in this perspective. Are you interested about origin or Roser equation or not?

    Are you still interested, what the "Open Science" means?

  28. Please feel free to delete all my posts, as I've backup copy already.

    I'll use this discussion (like many others) to analyze the source of conceptual problems of contemporary physics later.

    You know, anger and excessive arrogance isn't very tactical stance here.

  29. so I don't understand quite your question. Do you?

    Zephir: I have not deleted yet any of your comments in this thread, so what are you complaining about? I have deleted comments of yours on other threads because you had added links to your site which I count as spam.

    Were you just saying Hitler's use of "we" referred to his husband and him?

  30. You know, anger and excessive arrogance isn't very tactical stance here.

    It's called projection.

  31. /*..I have not deleted yet any of your comments in this thread..*/
    OK - and I still appreciate it!

    I assure you, I'm not angry at all at anyone here - I just want to demonstrate some natural patterns in human communication, which prohibits us to exchange information more fluently.

    Anyway, have a nice day, Z.

  32. "Dopant separation" appears to be locally scaled (fractional coordinates within a unit cell; x/a, y/b, z/c) not absolute. Lowering symmetry with partial atom substitution (doping) creates a much larger superlattice unit cell. If the original active atom spacing was 0.5 nm, it remains 0.5 nm. If the superlattice unit cell is ten times larger on each side, that same 0.5 nm spacing is now ten times smaller by relative measure.

    Do you wish to draw supercon wires? Current materials are highly anisotropic lamellar (like clays). They have huge unit cells. They cannot be synthesized in situ like brittle niobium bronzes. They will not be ductile and cannot be drawn into wire.

    Phonon-coupled high temp supercons are not useful until somebody drastically changes their physical properties. Little's exciton-coupled organic polymer high temp supercons can now be trivially synthesized. They are condemned on untested theoretical grounds and "should not be synthesized" to look.

    BCS theory is remarkably robust. The BCS mechanism will not perform above ~25 K for thermal softening of photon modes. That is why MgB2, Tc = 39 K, was discovered by an undergraduate doing scut work and zero progress has been made over nine years since. Professional management demands theory be validated by experiment. Professional science demands theory be falsified by experiment. The Church is winning not by inflicting its dogma but by inculcating its methods.

    You don't synthesize stuff you are told to make, you synthesize stuff you need to have. Will MgB2's anionic boron web survive reaction with dodecyl dimethyl chlorosilane or a reactive PEO oligomer? Now you have plastics solvent spinable as filament. Redox dope to restore mobile charges.

    Do Little, too. If they don't work you lost a lab week or two. If they do work you will be discharged for cause - insubordination. That is why "cutting edge" research is now chronic unproductive crap.

  33. Cosmologically I am one staring toward the heavens, while theoretically trying to reproduce the event on earth? :)

    The second phase brings the sector to 4.5 K using enormous refrigerators. Each sector has its own refrigerator and each of the main magnets is filled with liquid helium, the coolant of choice for the LHC because it is the only element to be in a liquid state at such a low temperature. See:For the first time the LHC reaches temperatures colder than outer space

    Like "three body problem" and Lagrangian identification of "fastest satellite pathways" bring to my mind the Meissner effect.

    Viscosity and fluidity of transfer and relations, would help conceptually such inclinations to temperature and particulate "impurity additions" to detail such freedoms of transfer of info? Tunneling? As well to identify metallic origins contain in the earth too, change "object differentiation," as a method to future travel?

    Particulate experimentally measured as to resistance and temp variation?

    LHC proton/proton collisions and speed of light.

    One is trying to "push back perspective?" Top down.

    Limitations had been reached to identify faster then light in mediums and resulting info in backdrop measures(Ice and Sno). At what point?

    Help to ascertain moments within supernova explosions to identify gravitational beginnings? How far into the event?

    Researchers hope to use the detection of neutrinos from the next nearby supernova to pinpoint the moment when gravitational waves--which have never been directly observed--should be detectable.


  34. rosers equation and godwins law
    ...two eternal mysteries

  35. ......It is considered poor form to raise such a comparison arbitrarily with the motive of ending the thread. ...

  36. Zephir,

    I had no time to read to this long comment thread over the day, and indeed, it is exactly as my wife said, Stefan said he doesn't believe a word because you haven't provided a reference.

    To get back to the starting point of this exchange, did you claim that the superconductors with the highest known transition temperatures are quasicrystals, or did you not?

    To my knowledge, there are quasicrystals which are superconductors (no wonder, as most non-magnetic metal alloys show superconductivity at low enough temperatures), and the situation for metallic glasses may be similar.

    But now, also to my best knowledge, the layered cuprate and iron pnictide superconductors are neither quasicrystals nor metallic glasses. If I am wrong, please correct me and hint me to the relevant crystallographic references.

    You are of course free to claim otherwise, but as it seems that you then will have to convince not just me, but thousands of mineralogists and crystallographers, you better provide solid data and evidence for this claim, and more than a reference to some "aether wave theory".

    Best, Stefan

  37. Bee and Stefan,

    This is a great post and the physics could well be timely. I encourage you to exercise your authority as the maestri, mavens, whatever, of this blog and not try to inject information into impenetrable skulls. Please follow Georg's excellent advice.


  38. Hi Zephir,

    your last few comments have been deleted, because (1) we don't appreciate promotion of private theories via links, as has been announced to you before, and (2) I was just shocked a bit to see that this post appears prominently when googling for the substance allegedly showing a record superconductive transition temperature of 185.6 Kelvin. Frankly, this claim is now one year and a half old, occurs on an obscure website only, and I have not the impression that any details have been published or that there has been any independent confirmation. I do not want this post to promulgate information I judge unreliable, misleading or outright false on important issues as this one.

    Actually, when you have read my original post attentively and came to the conclusion that the Röser formula, at the end of the day, may boil down to numerology, you have got the point.

    Thanks, Stefan

  39. Thoughts on the universe:)

    Run-of-the-mill compound becomes superstar.

    Historically one had to know where such excitement begins and then looking at periodic table one wonders even further at what is displayed for our viewers in the supernova to have been witness to something in the milliseconds that exists before, as to what's now measured .

    What shows itself first in elemental consideration that such transmission could have said, "this element first" and then, "this one."

    So not only do you push back time, but you look to what was "easily transmitted," before "time" essentially began?


  40. Phil,

    The ecosystem of science needs many different species of personalities and abilities.

    On top of that comes the issue of how best to organize them.

  41. Clifford of Asymptotia has a new entry which may be of use in the further study here.



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