The Antiferromagnetic Phase and Mott Insulators

There are certain compounds which, according to conventional electronic band theory of metals (which is usually quite successful in describing physical phenomena of materials), are predicted to be metals but are in fact insulators. In the 1930's/40's, Nevill Mott proposed that such substances could be insulators if one took into account electron-electron repulsion. Energetic electrons might want to hop from site (atom) to site in a lattice (array of atoms which make up a crystal) due to their thermal energy, but a repulsive potential (for example, the Coulomb potential) for electrons on a particular site (with opposite spins) may prevent this particle motion.

In particular, let us denote the "probability" of hopping of an electron to its neighboring site as "t" and the strength of the Coulomb repulsion to be "U". Then, a competition between t and U will determine whether a certain sample in a particular phase is conducting or insulating. This can be visualized in the diagrams to the left and right. In the first diagram, the electron (represented by an arrow) wants to hop to a neighboring site due to the kinetic energy t. However, even if the electron succeeds in hopping (second image), the Coulomb interaction U might be simply too large and the particle would then be pushed right back to the site where it started. This confines most electrons to their current sites, allowing no motion even at half-filling (a condition often giving rise to a conductor), and therefore the compound is insulating.

The electron-electron interaction doesn't have to be a Coulomb potential for this effect to occur. It could be something else, such as a magnetic (spin) interaction. The superexchange energy, which is a magnetic energy of repulsion (usually represented by J), can also prevent motion of particles from site to site when a sample normally might be expected to conduct. Such a situation is the case in an antiferromagnetic insulator. Antiferromagnetic insulators exhibit insulation through the same kind of effect as in the Coulomb potential case, and they are in fact Mott insulators themselves. Antiferromagnetic insulators exhibit Neel order (shown in above two diagrams), which is a configuration of valence electronics in a lattice for which every spin alternates from site to site.

What does any of this have to do with high-temperature superconductivity? Well, go back to the page on cuprates and take another look at the phase diagram. It turns out that, for zero or low doping, the high-Tc cuprates are in fact antiferromagnetic insulators! Because they are most likely Mott insulators, the problem of high-termperature superconductivity and the problem of understanding doping of a Mott insulator are probably very interrelated.

Next: The "Pseudogap" Phase