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.
How 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.