- What is the mechanism for HTSC? That is, how does it work?
- Can we find a superconductor that works at even higher temperatures, like room temperature?
So my perspective is very limited. Superconductivity is a vast field, and I occupy one tiny little corner. I don't have a great idea of the big picture, because I'm too busy trying to understand the details of the stuff near my own corner. And I don't even fully understand that. Consider this a distorted portrait.
What "unsolved" means
In fact, superconductivity is already understood. It was solved in 1957, when BCS theory was proposed. BCS theory is named for its creators: Bardeen, Schrieffer, and Cooper. The solution is that electrons pair up. In order to pair up, there needs to be an attractive force between electrons. There is an interaction between electrons and the ionic lattice that creates an effective attractive interaction between electron pairs.
But superconductivity reasserted itself as a mystery with the discovery of HTSC in 1986. BCS theory does not work for HTSC materials. It does not predict that superconductors could exist at such high temperatures (ie minus 140 degrees celsius). We need a new theory of superconductivity for the newly discovered materials. But it's not completely up for grabs. We're still fairly sure that electrons must be pairing up due to some effective attractive interaction. We're just unsure where the effective attractive interaction comes from.
Mind you, when I say low-temperature superconductivity is "understood" and high-temperature superconductivity is not understood, I'm not referring to my personal level of understanding. I don't really understand BCS theory. That is to say, I don't know how to calculate the electron-phonon interaction, and I don't know how to get from the microscopic theory to the Ginzberg-Landau theory. But that previous sentence might have been gibberish to most of you. Perhaps what I call "not understanding" is a much deeper understanding than the most educated lay person.
Surely when HTSC is solved, the solution will involve all these little technicalities. I will not be able to understand the solution. I will understand the cartoon picture that accompanies the solution, but I will not understand the calculations.
An excess, not a scarcity, of theories
People generally don't talk about mechanisms for HTSC. The expression "elephant in the room" comes to mind. My impression is that lots of mechanisms were proposed around 1986-1990, and then it became unfashionable. The problem isn't that we don't have a theory, it's that we have too many theories. We need evidence to knock down some of those theories.
New mechanisms for HTSC are occasionally proposed on ArXiV (which is where most physicists share their upcoming publications). I often wonder if these are cranks. There's nothing really to stop cranks from putting things up on ArXiV, since it's not peer-reviewed. I'm told there's even an unwritten special section for cranks (the "general physics" section). But perhaps many of these papers are completely legitimate and respectable. The point is I wouldn't be able to the difference. I've never gotten the impression that they have high impact anyway.
At March Meeting (a huge condensed matter physics conference with over 8000 talks) a few weeks ago, I saw a couple proposals for HTSC mechanisms. One proposal was made during a 12 minute talk trying to explain the observations of some recent experiment. The talk sounded exciting, but I didn't understand it at all. That's not unusual; I don't understand most of the talks.
The other proposal occurred in a poster presentation. The guy had a theory that did not involve electron pairing. That makes it "wacky". I had the impression that he was sort of a crank, since he said he was unable to get published or get funding. But I respected him anyway. I don't understand BCS theory, and I didn't understand his theory. If I'm honest, I can't argue with him. Let the knowledgeable theorists do the arguing.
I mentioned my impression that people don't really talk about mechanisms for superconductivity. He said that's because everyone thinks superconductivity is already solved, and that the solution happens to be the idea they themselves proposed. He alluded to (Nobel Laureate) Phil Anderson's theory. I'm told that Anderson's mechanism involves electron pairing, but a repulsive force is sufficient to allow the pairing. That sounds "wacky" too, but what do I know?
Approaching the problem indirectly
Earlier I said that as an experimentalist, I just test ideas proposed by theorists. But we don't really talk about mechanisms for HTSC. Instead, we test smaller ideas.
For example, one of the big debates is about a "kink" in the electronic structure. Is it caused by an interaction between electrons and phonons, or an interaction between electrons and magnons? And is it related to superconductivity or not? I suppose there must be a class of theories involving phonons, and a class of theories involving magnons, but we don't talk about the theories directly. We're just trying to establish the basic facts.
Another big debate is about the so-called "pseudogap" state, which is a strange state that has been observed above the superconducting temperature. What is the nature of this state of matter? Is it competing with superconductivity, or is it perhaps an incipient form of superconductivity? Perhaps it has something to do with CDWs or stripes? Not that any of this makes sense to you unless you're in the same field as me. But once we figure out the answer, I'm sure I'll be able to draw a cartoon of it that you'll understand.
I think when we think of historical physics discoveries, we often think of the Eureka! moment. Someone writes a great paper, and all the problems are solved as it clicks into place. I'm suspicious of this narrative, because that's not how the field of HTSC looks. It will be a slow and incremental progression. Slowly working out incomprehensible technicalities. But afterwards it will have looked simple. We'll have a nice cartoon, and we'll tell stories about the scientists who, in a flash of brilliance, dreamed up those cartoons.