Detour Into Normal Superconductors

Last Thursday night, I witnessed by accident a pretty interesting conversation. Two young men, called Peter and John, were having dinner together at a Diner. I was quiet in the table behind them, listening to the conversation. While enjoying a quite delicious cookies ‘n cream shake and a succulent bacon cheeseburger, they started chatting about a great new blog they found on the internet, called Quantum Matters. John just read some very good posts on superconductivity on the blog, and decided to make a few questions to Peter, who happened to be a physicist and had worked for a while on high .

John:

So Peter, as I was telling you, I was reading two posts they have on superconductivity. They started talking about the parent state of cuprate superconductors, and moved from there to talk about the pseudogap region. Nonetheless, the posts stopped there. Right when they were reaching about 8% doping, they let us readers hanging, saying we should stay tuned. I will definitely stay tuned, but I am quite anxious to know the end of the story! So, how does the game continues? What is the deal after I dope the material past the pseudogap phase?

Peter:

Well John, the “magic” is that close to 8% doping, these materials, which in their parent state are insulators (and even in the pseudogap region their conductivity is nothing to brag about!) become the best conductors in the universe! The temperature at which they lose superconductivity varies with doping. It begins increasing at about 8% doping, reaches a maximum close to 20% doping, and then decreases to zero again, forming a dome.

John:	How does that happen?
Peter:	Ok, let’s change things a bit here and better than talking about the particular case of cuprates, let me explain you what happens in normal superconductors, for cuprates are a little bit special. At very low temperatures, electrons in a normal superconductor like to bind in pairs. It turns out that they lower their energy when they are paired. And in physics my friend, everything is governed by energetics. So an electron with momentum and spin up () pairs with an electron with momentum and spin down (). The pairs are called Cooper pairs.

John:	Wo, wo ,wo! Wait a second! Excuse my ignorance, but according to one of the first things I learned about physics in high school, electrons repel each other. How can they bind in pairs then?
Peter:	I see you are awake and alert! Well, there are two things in here. Electrons interact among themselves via an electric force, or Coulomb interaction, which is indeed repulsive. On the other hand, they live in a material made of atoms. And the atoms form a lattice. The ions in such lattice can vibrate, and such vibrations behave as quantum particles called phonons. This is analogous to light being a wave which also behaves as a quantum particle called photon. Electrons can feel such vibrations, and in fact, they can “talk” to each other by exchanging phonons. In such a way, they can feel an attractive interaction among themselves. See how it works John? They can attract each other via the mediation of a phonon. That’s how they bind in pairs.
John:	Ok, so we have these Cooper pairs. Now, how do they lead to superconductivity?
Peter:	Ahh, good question! But before I tell you, would you order a basket of onion rings? You know, knowledge costs something!
John:	What a briber!
Peter:	Ok, it turns out that these Cooper pairs, like any other particle in quantum mechanics, have a wavefunction associated with them. And this wavefunction naturally has a phase. In a superconductor, not only electrons are paired, but all pairs’ wavefunctions have the exact same phase. And it costs a whole lot of energy to change that phase. That is what gives the rigidity to the ground state (or fundamental, i.e. lowest energy, state), which in turns allows it to superconduct. This is because once a current is set in the material, changing that current implies changing the phase of the Cooper pairs, which is simply energetically too costly. Hence, the current stays there forever, unaltered. See, the same principle is what is responsible for a superconductor being able to levitate a magnet. If you try to put a magnetic field through a piece of superconductor, the superconductor hates it, because it means changing their phase. It prefers to set up a current along its edges, which in turns produces a magnetic field opposing that of the magnet, and expel the field of the magnet. And voilà! The magnet levitates! Impressive isn’t it?

Photo from Lawrence Berkeley Laboratory. Click here for photo source

Well my readers, there you had it. Quite an interesting conversation! Nonetheless, there is another important and quite cool phenomena exhibited by superconductors, which Peter forgot to tell John about. But that is why I’m here. You guys have Damian to tell you.

It turns out that if you take two pieces of superconductors, different superconductors, with different , and put them in contact, so that you form a junction out of the two pieces, there is current flowing from one side of the junction to the other, even if you apply no voltage at all! Surprised? Well, you should be! The reason there is current flowing even with no voltage is that the Cooper pairs in each piece of superconductor have the same phase within that piece, but such a phase is different from the phase in the other piece of superconductor. When you put both pieces together, because they like to have the same phase all over, they try to equalize the phase across the junction. This causes the current. The effect is called Josephson tunneling, for the pairs in one side tunnel to the other side through the junction. I should mention briefly that the Cooper pairs can only tunnel if their spins are paired in the same way inside the pairs (that is, an up spin with a down spin for example — called a singlet –, or two ups, or two downs — called a triplet –, etc). This was an important experimental tool which allowed physicists not only to determine the type of pairing in different superconductors (knowing the pairing of one of the superconductors, you can tell the pairing of the second if Josephson tunneling occurs), but to make intelligent guesses on whether cuprates are really Cooper paired or not. But this is a subject that requires a bit of explanation. I’ll tell you more about it in my next post.

Till then,

Dr. Damiam Rudelberg