How Do Superconductors Work?

In the reader request thread, Brad asks about superconductors:

Why is a room temperature superconductor so hard? Why do things have to be cold for there to be no resistance (I can guess, but my knowledge of super conductors consists of the words “Cooper pairs” which does not get me very far.)

Since next year will mark 100 years since the initial discovery of superconductivity in mercury by Heike Kammerlingh Onnes, this is a good topic to talk about. Unfortunately, it’s a bit outside my field, but I can give you what I know from my not-much-better-than-layman’s understanding of the field, and that will probably provoke some additional information in comments.

What is a superconductor, anyway? A superconductor is a material with zero electrical resistance. That is, when you send a current into it, that current flows straight through it as if it weren’t there. Better yet, you get persistent currents– if you start a current flowing in a loop of superconductor, it will keep flowing forever, unlike a normal conductor, where losses to heat and so on will cause the current to dissipate pretty quickly unless you do something to keep it going.

That sounds pretty awesome. Useful, too. So, how does it work? It took a while to figure out what’s going on, but one of the key bits of information is that the transition from a normal material to a superconductor happens abruptly, at very low temperature. This suggests that it might somehow be associated with another weird phenomenon that happens at extremely low temperatures, Bose-Einstein Condensation.

In Bose-Einstein Condensation, when the temperature gets below some critical value, a gas of bosons will suddenly make a transition to a state where all the atoms in the gas occupy a single quantum state, the lowest energy state available.

(This, by the way, is what a famous theorist termed the “high school physics” version of what BEC is (by telling Bill Phillips that he needed to stop thinking of BEC in terms of high school physics). More formally, the transition is characterized by “off-diagonal long range order,” as there are condensed matter systems where the macroscopic-occupation-of-the-ground-state explanation doesn’t work. For the purposes of this explanation, though, high school physics will be more than sufficient.)

OK, that sounds sort of plausible. Doesn’t BEC require the particles to be bosons, though? And didn’t you just get done explaining that electron spin makes them fermions? How can you get a whole bunch of electrons into a single quantum state? That’s the tricky part. You need some way to turn electrons from fermions into bosons if you’re going to invoke BEC physics to explain superconductivity.

The way to do this is to pair the electrons up. The characteristic spin behavior of electrons is what makes them unable to occupy the same quantum state in large numbers, but if you put two electrons together in the right way, you can make a composite particle with either no spin at all (one electron spin-up, the other spin-down), or a spin of 1 (both up or both down). That composite particle is a boson, so you can make a BEC of electron pairs, and use that to explain superconductivity.

OK, but how do you stick two electrons together to make a boson? They repel each other, don’t they? Two isolated electrons do repel each other, but two electrons in a superconductor aren’t isolated– they’re in the middle of a huge lattice of positively charged atoms making up the solid.

And that’s the key. Two electrons by themselves can’t be stuck together, but two electrons inside a lattice can develop an attractive force between them that’s mediated by the lattice.

i-975a3b4add828a3e36f33c47b590bc61-bcs7.gifHow does that work? If you imagine the atoms making up a superconductor as being like a regular array of positive charges held more or less in place, but free to move by small amounts, an electron passing through the lattice will distort things slightly, as in the image at right, which I stole from hyperphysics. The atoms in the wake of a passing electron are pulled toward where that electron used to be.

A second electron coming along will see that disturbance in the lattice, and have its trajectory altered by it. The net result is to pull the second electron toward the first, and vice versa, creating a small attractive interaction between them. That lattice-mediated interaction is what causes the electrons to “pair up.” The resulting pairs are called “Cooper pairs” after Leon Cooper, who worked out how this would happen.

OK, but why doesn’t that just happen all the time? Why do you need the sample to be cold? the Cooper pairing mechanism depends on displacements of atoms in the lattice due to the passing electrons. At high temperatures, though, the atoms in the lattice are moving all over the place all on their own– the temperature, you remember, is a measure of the energy of the atoms making up a substance. High-temperature materials have their atoms vibrating by too much for the tiny tug of a passing electron to create a significant effect. In order for Cooper pairing to work, the solid needs to be cold enough that the tiny additional motion caused by a passing electron is large compared to the thermal vibrations.

(More formally, condensed matter physicists talk about “phonons,” which are the lattice vibration equivalent of photons of light– the particle model of a propagating disturbance (an electromagnetic field for photons, a vibration in the lattice for phonons). In the phonon picture, the vibration of the lattice is expressed in terms of numbers of phonons in various modes– a high-temperature sample has lots of phonons present, a low-temperature sample very few. The Cooper pairing mechanism requires you to have few enough thermal phonons in the relevant modes for the phonons created by the motion of electrons to be the dominant source of vibration near the pairing electrons.)

Once you get cold enough for the pairing to take place, you also need the pairs to be cold enough to Bose condense, but that’s not usually a problem.

OK, so what are high-temperature superconductors, then? The best theory we have of ordinary superconducting materials is known as “BCS” theory after the names of its inventors– John Bardeen, the aforementioned Leon Cooper, and John Robert Schrieffer (fun fact: the Nobel they shared was Bardeen’s second– he also shared one for the invention of the transistor). The BCS mechanism explains superconductivity in ordinary materials, and predicts the superconducting transition temperature and other properties very nicely. Unfortunately, the maximum transition temperature predicted with BCS theory is something like 30 K– thirty degrees Celsius above absolute zero, or around -405 degree Fahrenheit, for my fellow Americans. That’s obtainable in experiments using liquid helium, but not something you’re going to run into very often.

In the mid-1980’s, though, a new class of high temperature superconductors was discovered, with transition temperatures as high as 100 K, which is a temperature you can reach with liquid nitrogen (which boils at 77K). Suddenly, superconductivity was within reach of anybody with a couple hundred bucks and access to liquid nitrogen.

How does that work, though? If BCS theory limits you to 30K, how do you get above 100K? To quote a cosmology professor I had as an undergrad, in a different context, “I do not know this. If I knew this, I would be in Stockholm.” There are a lot of theories that attempt to explain high-temperature superconductivity, but none of them are entirely successful. Whoever finally figures it out is pretty much guaranteed a Nobel Prize very shortly thereafter.

It’s a difficult problem, because the materials that superconduct at high temperatures are pretty weird– they’re ceramics, not metals like ordinary conductors, and they involve some strange elements (lanthanum, yttrium, barium). They also have an odd layered structure, consisting of two-dimensional sheets of different atoms, making it tricky to describe theoretically (the materials described with BCS theory tend to be relatively uniform). This structure is presumably critical to whatever mechanism allows them to superconduct at high temperatures, but exactly what’s going on hasn’t been worked out yet.

So, just how high is it possible to get? Nobody knows. You can find people claiming room temperature effects, like this recent arxiv paper, though none of them are terribly convincing. Without a good theory of what’s going on, we can’t say for sure what the limits are.

Wouldn’t room temperature superconductivity be an awfully big deal? That’s an understatement. If reliable superconductivity could be produced at room temperature (the transition temperature should ideally be a bit higher–310 K or better), it has the potential to revolutionize everything. We’re talking lossless electric transmission lines, levitating trains, absurdly efficient electronics of all sorts. Assuming such a material could be found and produced in large quantities, it’s not unrealistic to call it a trillion-dollar possible industry.

Of course, there are an awful lot of “if”s in that paragraph. That’s why there are so many condensed matter physicists working on the problem, both by trying out new theories, and by playing around with different sorts of materials to see if they can stumble on something that will unlock the whole mystery.

That sounds a whole lot more useful than a Higgs boson. Unsurprisingly, I agree. It’s a tough problem, though, and a hard one to explain, especially at the high-school-physics level. I hope this at least provides some hint of what’s going on, and why it’s tricky, though.

Comments

  1. #1 Pineyman
    August 3, 2010

    For a NMBTL understanding, this was a fine, lucid explanation. Thanks.

  2. #2 jerry anning
    August 3, 2010

    Whenever I read about high temp superconductors, the articles refer to several competing theories or words along that line. Why haven’t the clunkers been weeded out by experiments? Nonquantitative? Predictions too hard to generate? Effects too subtle for current technology? Some other reason(s)?

  3. #3 Moshe
    August 3, 2010

    The person asking the questions may be interested to know that particle accelerators are powered by huge superconducting magnets, and accelerator physics and/or engineering is in large part understanding how these work, and how to make them useful (knowledge which then percolates to society at large). As a pedagogical point, maybe that will go a small way towards discouraging that guy’s either-or approach to intellectual pursuit. But if he still wants to be useful, making slightly cheaper cardboard boxes is probably much more useful than any of this stuff.

    But, nice explanation overall. I think some people (e.g. Tony Leggett) will take issue with the whole “BEC of Cooper pairs” picture, but any alternative explanation is probably a lot less intuitive.

  4. #4 Braden
    August 3, 2010

    One important addition: a superconductor is not merely characterized by lossless conduction. A perfect conductor also has lossless conduction. What superconductors have over perfect conductors is the Meissner Effect: the expulsion of mangetic fields when the superconductor enters the superconducting state. Perfect conductors don’t do this, hence the distinction.

  5. #5 D. C. Sessions
    August 3, 2010

    Wouldn’t room temperature superconductivity be an awfully big deal? That’s an understatement. If reliable superconductivity could be produced at room temperature (the transition temperature should ideally be a bit higher–310 K or better), it has the potential to revolutionize everything. We’re talking lossless electric transmission lines, levitating trains, absurdly efficient electronics of all sorts. Assuming such a material could be found and produced in large quantities, it’s not unrealistic to call it a trillion-dollar possible industry.

    Yes and no. Room-temperature superconductors would be useful for low-power applications regardless, but to be useful for power applications they would also have to have a high critical field intensity. A critical field in the fT range would be handy for switching electronics, but useless for power systems.

  6. #6 Chad Orzel
    August 3, 2010

    Whenever I read about high temp superconductors, the articles refer to several competing theories or words along that line. Why haven’t the clunkers been weeded out by experiments? Nonquantitative? Predictions too hard to generate? Effects too subtle for current technology? Some other reason(s)?

    A combination of difficult predictions and subtle effects, I think. Again, I am not a condensed matter physicist, but my impression from years of occasional press releases touting new results is that evidence for one theory or another is really difficult to generate, and what evidence exists is slightly muddled, sometimes looking like it supports one version of things, and sometimes another.

    The person asking the questions may be interested to know that particle accelerators are powered by huge superconducting magnets, and accelerator physics and/or engineering is in large part understanding how these work, and how to make them useful (knowledge which then percolates to society at large).

    The person asking the questions likes to throw the occasional late curve ball, just to see how many people are reading all the way to the end.

    One important addition: a superconductor is not merely characterized by lossless conduction. A perfect conductor also has lossless conduction. What superconductors have over perfect conductors is the Meissner Effect: the expulsion of mangetic fields when the superconductor enters the superconducting state.

    Yes, absolutely. This is the lies-to-children version, and I was trying to keep the post as simple and concise as I could.

    The Meissner Effect is, of course, the core of the standard high-Tc superconductor demo, namely the levitation of a small magnet over a chunk of superconductor. Or the cool little superconducting “train” they had at the Perimeter Institute’s Quantum to Cosmos demo tent, with a superconductor car riding on a track of magnets.

    (In very rough terms, a magnetic field trying to enter a superconductor will create a small loop of current that produces a magnetic field in the opposite direction. The interaction of this field with the field of a nearby magnet creates a force pushing the magnet away from the superconductor, which can be used to float a magnet above a chunk of superconductor, or vice versa.)

  7. #7 Richard
    August 3, 2010

    jerry anning: I think there are lots of theories that can plausibly explain high-Tc superconductivity, it’s just there haven’t been any experiments that have definitively picked one over all the others (I’m sure there have been some sensible proposed theories that have fallen by the wayside). A lot of the theories are based on simple models and even with the simplifications they’re quite complicated so I think it’s quite difficult to just say which one is right by looking at it.

    The “BEC of Cooper pairs” picture is the only way I have any understanding of anything, I think..

    Regarding the last paragraph, the Meissner effect is due to the (Anderson-)Higgs mechanism so in some sense a superconductor is both useful and has a Higgs boson. Sort of.

  8. #8 Moshe
    August 3, 2010

    Ah, but some people may start at the end, trained by alphabetical author lists that may include a certain W. Anyhow, I take your point, so I’ll avoid pointing out that the Meissner effect is in fact the non-relativistic version of the Higgs mechanism.

  9. #9 Mary
    August 3, 2010

    Chad, I like this post, but I am still confused (as I have been by similar explanations I’ve heard in the past) about why the resistance actually drops to zero. I mean, okay, so I’ve got a “BEC of Cooper pairs,” and it has to be cold for that to happen — got it. So what? BECs can scatter off of things. Why don’t the paired-up electrons, or the super-particle made of paired-up electrons, scatter off the atoms in the lattice any more? What am I missing?

  10. #10 Brad
    August 3, 2010

    Thanks Chad!

    The BEC of Cooper Pairs (and the nice explanation of what a Cooper Pair is) was great!

    Now if you could only answer my stat mech question…..

  11. #11 Rolando
    August 3, 2010

    @Mary: the reason why there is zero resistance is that in fact a superconductor is not simply “made up” of Cooper pairs that go BEC (this is a nice picture, but it doesn’t provide the full picture which is rather complicated). One should see a SC as a collective/macroscopic/quantum mechanical object that is superfluid, i.e. it responds as a single unit without dissipation. So, this macroscopic object does not easily scatter (it takes some amount of energy for this superfluid to scatter off anything, this energy is called 2*Delta), and so the superfluid can flow without resistance when no additional energy is supplied to it.

  12. #12 scramton
    August 3, 2010

    Getting matter to follow Bose Einstein statistics would be a test of high temperature superconductors.

  13. #13 Thomas
    August 4, 2010

    Why do room temperature superconductors get all the attention? An efficient thermoelectric converter would most likely have more impact on society, yet you rarely hear talk about them in popular science.

  14. #14 Chad Orzel
    August 4, 2010

    First and foremost, I somehow forgot to include a link to John Baez’s report on a talk by Tony Leggett that covers a lot of the issues in high-Tc superconductors. It’s notes from a talk, so it’s a little sketchy, but answers a bunch of questions asked here.

    Chad, I like this post, but I am still confused (as I have been by similar explanations I’ve heard in the past) about why the resistance actually drops to zero. I mean, okay, so I’ve got a “BEC of Cooper pairs,” and it has to be cold for that to happen — got it. So what? BECs can scatter off of things. Why don’t the paired-up electrons, or the super-particle made of paired-up electrons, scatter off the atoms in the lattice any more? What am I missing?

    I’m a little hazy on it myself, but I think the idea is that when you get the condensed state moving, there isn’t really another state for the electrons to go into. Any state other than the flowing-current one would have a higher energy, and the electrons (or Cooper pairs) can’t easily gain that energy from collisions with the atoms in the lattice (which don’t have enough thermal energy to knock them into a higher state) or with other electrons/Cooper pairs (they’re all already in the lowest-energy state, so there’s no way to have an inelastic collision excite one).

    I don’t have a good mental microscopic picture of why you get that gap, though. I don’t think it’s just the “binding energy” of the Cooper pairs, or anything simple like that.

  15. #15 Louis
    August 4, 2010

    @Thomas: Just to point out that high Temperature sc are what we called strongly correlated electronics systems and these kind of systems have usually pretty good thermoelectric properties. So, if you look at high Temperature sc in the normal phase, you could maybe have a good thermoelectric converter. Using materials that are strongly correlated electronic systems for their thermal properties could be a major everyday life application for these really exotic systems. I’m not saying that the Cuprates will be necessary the system of choice because there are plenty of other types of strongly correlated systems.

    About your question on why: “Why do room temperature superconductors get all the attention?” I can tell you my view. The hype is not that much about how we could used them to improve already existing device like electrical wire for example, but much more about everything we could create that we have not yet thought about. It may seem a little confused, but let me clarify my point. The hope is that room Temperature sc could drive a real technological revolution in its real definition. By this, I mean, for example, the transistor. When it was invented in 1947, they knew it was a useful device but they could never predict what this invention could lead 60 years later (for example)-> complicated electronic circuits -> computer (smaller then a room) -> Internet -> Google … The transistor is now a part of almost everything we use. This was possible because in the forties, peoples started having a good enough understanding of the semiconductors to be able to make some predictions. So here the hopes, we now have these systems, high Temperature sc, that have extremely exotics properties, much more exotic than semiconductors. If we can make predictions, the possibilities for peoples to invent new, never thought about, applications is tremendous. Improving already existing device is really great and for sure, we should work on it a lot. But it is the possibilities that we do not know yet that make these materials so fascinating.

    Sorry for the long post

  16. #16 Thomas Lee Elifritz
    August 4, 2010

    One word young man : Mottness.

    That, and the BCS to BEC (BOSE) transition.

    You need to educate yourself a little more before you start baffling the rubes with …

  17. #17 Louis
    August 4, 2010

    @ Thomas Lee Elifritz

    I do not really follow your point, could you elaborate? If your point is about cuprates not being good for thermoelectric application at room temperature, I agree that the figure of merit is not that good and it is why I said it is not necessary the strongly correlated system of choice. Materials like NCO are probably better.

    But Mottness is not necessary bad for thermoelectric application. It is for many systems but not always.

  18. #18 iastos
    August 4, 2010

    Couldn’t RT SuperCs could enhance quantum computers by eliminating power loss to a state where, with added higher degeneracies beyond binary (spintronics), we might have the computing power and memory to upload large, hyper-complex systems such as human personalities (individuals and ppopulations)?

    But wouldn’t the removal of power loss reduce the thermodynamics of computing (information creation and transmission) to just entropic terms, i.e., non-enthalpic? And what would this mean?

  19. #19 Thomas Lee Elifritz
    August 4, 2010

    The point I’m trying to make is that the phenomenon of superconductivity comes in many flavors, from wide band, narrow gap metallic systems to extreme Mott materials that may or may not involve antiferromagnetism. Mott transitions (or alternatively, metal – superconductor – insulator transitions) come in many forms as well, pressure (density) induced, temperature induced, doping induced, disorder induced, and various field induced (take your pick), etc., and now with advanced high resolution ARPES techniques we see orbital selective Mott transitions abounding in the data. It now looks like there are several different quantum critical points hidden under the superconducting dome, so there are cosmological implications as well (think black holes and their event horizons) – in other words, the singularities are hidden, but they do exist, and physics itself appears to morph as you approach them (think special relativity), and all of this is applicable to high density exotic states of matter (again, take your pick, it really doesn’t matter).

    Thermoelectricity is but a small side show in this zoo of physics. It’s true that Tony Leggett kicked this off with his well known calculation of the ‘Leggett crossover’, but there were indications of something strange going on before that time as well. The earliest known paper is by D. Eagles, besides the obvious examples of Richard A. Ogg and early failed (I prefer prematures) theories. There was an interesting paper on failed theories just last night on the Arxiv.

    The trick with this, is to create stable materials that approach the BCS-BEC transition without falling apart, phase separating, exploding, reacting, disproportionating, etc., and the cuprates are already on the bleeding edge, which is why we are observing their microscopic inhomogeneities. Even ordinary Bi/Te thermoelectrics have those issues.

    When you transfer spectral weight across the Mott gap, you are dealing with energies in the 3 eV range, and the charge transfer gaps are also quite large (running all through the optical) so you have to be careful. That’s why chemists are leading the way though the wilderness with this subject. Coherence at those energy scales and at high density can be quite dangerous, as anyone working a super battery knows.

  20. #20 Paul
    August 5, 2010

    Moshe: “…the Meissner effect is in fact the non-relativistic version of the Higgs mechanism.”

    I wouldn’t put it like that, the Meissner effect is the *real* physical phenomenon discovered in 1933.

    The Higgs mechanism is a speculative theoretical idea developed in 1960s and modeled on the Meissner effect.

  21. #21 Cody
    August 5, 2010

    Thanks for this, your explanation fits together a lot of the very small pieces I understood previously.

    I’m not sure anyone has said this, but since the Cooper pairs are bosons, they don’t follow the Pauli exclusion principle, and there can be many of them occupying the same state, (or more magically the same position in space), right? So there is no real limit to how much current you cram into one circuit after that, or am I wrong about that…?

  22. #22 saweela aamir
    September 28, 2010

    im a teenager and i need to do a project on super conductivity i have seen various sites and this is by far the most understandible but what i still do not get is that what is the highest temp at which superconductivity has taken place? can some one please ans that
    thank you:)

  23. #23 saweela aamir
    September 29, 2010

    I am a student of ordinary level and I have a project to do on superconductors. I have searched many sites & links but this is by far the most helpful site except it does not say what is the highest temp at which a superconductor can work.
    Mr Chad could u please tell me?
    thank you

  24. #24 Jon
    October 4, 2010

    thanks for this article, was really nice to learn a bit more about this after reading a short description in my physics book.

  25. #25 Sam
    November 8, 2010

    As of now, the best superconductor is (TI4Ba)Ba2MgCu8O13+ and it superconducts at 268K (Kelvin) -8 Celsius. This is a 9223 struture if you know what that means. I need someone to identify the structure parts i.e. the 9 and email me at sazsal09@yahoo.com.au. An image of the superconductor can be found at this website: http://www.superconductors.org/265K.htm.

    Thankyou

  26. #26 Carolin
    October 5, 2011

    I really don’t understand how BEC relates to Superconductors …

    can anyone explain this?

  27. #27 ASHWIN
    January 31, 2012

    I Have an doubt
    that superconductor can be used in roads
    by making the roads into yttrium BARIUM copper oxide (which is non magnetic At normal room temperature ) and pouring liquid nitrogen will make the magnetic object to flow
    in the concept of saving a petrol by designing the road into yttrium BARIUM copper oxide material and our car/bike is redesign into magnetic material by keeping the heavy magnet under the bike/car…and removing of tyres so that leviation is to leviate approx 170mm

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