# What DO We Know About High Tc?

Many papers on cuprate superconductors start out by saying that we don’t know much about them. About ten years ago, A.J. Leggett wrote down a laundry list of things we do know. Looking at this list, it seems like things are not as bleak as the introductions to papers on cuprates make them out to be! Here is his list of things we knew back in 2006:

1. Superconductivity in the cuprates is a result of Cooper pairing.
2. The main driver of superconductivity in the cuprates is the copper-oxide plane.
3. To a good approximation, Cooper pairs form independently on each layer (even in a multilayered compound) in the cuprates.
4. The net saving of energy in the transition to the superconducting state is not from ionic kinetic energy as in the classic BCS superconductors. (This surprising result in BCS superconductors was shown to be true in this paper.)
5. The spin state is a singlet.
6. The order parameter is of $d_{x^2-y^2}$ symmetry.
7. The size of Cooper pairs is somewhere between 10-30$\text{\AA}$.
8. The pairs are formed from time-reversed partners as in BCS theory.

There is one more aspect of this paper that I think is significant. Leggett stresses the importance of asking questions that are model-independent, such as, (1) What is the pairing symmetry? (2) Does the macroscopic Ginzburg-Landau theory work? and (3) Where is the energy saved in the transition to the superconducting state? Posing questions like these are the “tortoise” method versus developing microscopic theories, which are the “hare’s” method. With the existence of so many microscopic models, it seems to me that taking the “tortoise” path may yield fruit in the long term.

I have been told by a number of my peers that I apparently like lists, which is probably why this article sticks out in my mind. Between the time this article was written and the present, are there any additional items to add to the list? I’m not an expert in high-Tc, so I’m wondering if there is more we now know. Many experimental signatures spring to mind, but none that I would necessarily say that we know “for sure”.