On High Temperature Superconductivity: The Parent State

How about giving our second step in the race through the “quantum world”? We propose it to be into the amusements of High Temperature (high ) Superconductors. For those not familiar with the topic, do not worry. We’ll start, of course, by providing you with a review of the basic properties of high temperature superconductors, so you can feel comfortable following us in future posts where we will be commenting actively on experiments, theory related to experiments, and so on.

Imagine a having a material where you can set up a current, and such current will never decay! No resistance, no energy dissipation, wait for as many years as your life allows you, and the current stays there, unaltered. Imagine the same material levitating a magnet!

Magnet levitating on top of a piece of superconductor. Photo from Lawrence Berkeley Laboratory. Click here for photo source

Sounds like fantasy, like dreams, doesn’t it? Well, it is not. Nature has provided us with this wonder. These materials are known as superconductors.

And now you might wonder, what are exactly high temperature superconductors? How do they look like? Well, they are a family of materials which when undoped are insulating salts.

Piece of high temperature superconductor Bi-2223.Photo from Wikimedia Commons. Click here for photo source

Piece of high temperature superconductor YBCO. Photo from UBC Materials Research. Click here for source

They consist of Copper-Oxygen planes separated by a bunch of other elements in the structure between the planes.

Crystal Structure of Bi-2212. You can see here the Copper-Oxide layer, where Copper is shown in purple and Oxygen in brown. Stuff in between are Bismuth in green, Calcium in pink and Strontium in orange. Photo from Lawrence Berkeley Laboratory. Click here for photo source

The different families differ in the structure between the planes and also in the number of Copper-Oxide planes in the unit cell. There are materials with two consecutive Copper-Oxygen planes (these are denominated “bilayer superconductors”), and some with more consecutive planes (multilayer materials) in the unit cell. Because of the presence of the Copper-Oxygen planes, and their importance, as all the cool action happens in the planes, these materials are colloquially known as “cuprates”

The cuprates are interesting even when undoped. When undoped, the Copper-Oxygen planes have an odd number of electrons. According to standard band theory (which works for most materials), it should have an unfilled band and thus be a metal. The cuprates are not only not a metal, but are insulators with a very healthy gap! This is because the on-site repulsion is very large.

The large per Copper site prevents the electrons from tunneling from site to site, effectively leaving one valence electron per Copper site. Now, hybridization of the Copper atoms with the oxygen leads to a splitting of the valence band. The valence band now accommodates two electrons per Copper and is half filled. Having two electrons in a site costs energy and thus the insulator has a gap proportional to . The material is insulating due to strong correlation effects.

Materials like the cuprates that should be metallic, but are insulating are called Mott insulators in honor of Sir Nevill Mott who first recognized that electronic repulsion and its consequent strong correlation effects could turn metals into insulators. In fact, strong correlations among particles are the cradle of plenty of exotic, cutting edge materials physics. One could arguably state that the major part of modern day condensed matter physics is the study of strong correlations and the nontrivial physics that arises from them.

Now, even though there is no real tunneling in these materials, there is virtual tunneling driven by the lowering of kinetic energy of the on site localized electron by spreading somewhat to neighboring sites. This virtual tunneling leads to an effective antiferromagnetic interaction between the spins of the neighboring localized spins, which prefer to line up antiparallel to each other. The reason that the interaction is antiferromagnetic is that if the spins are aligned parallel to each other, the Pauli exclusion principle prohibits tunneling, be it virtual or real. This prohibition vitiates the possible lowering of kinetic energy due to localization. If the spins are antiferromagnetically aligned in neighboring sites, then tunneling fluctuations and their concomitant energy reduction can and does occur. This is the reason why the half filled, or undoped, cuprates are antiferromagnetically ordered Mott insulators.

We are ready to move now into where the action really is in this materials. But this will be the subject of another post.

Stay tuned for more!

Dr. Damian Rudelberg