phase are problems that will occupy much of the focus of CMMP in the coming decade.

If one could ignore the interactions between electrons in a solid, the properties of the material could be derived from a theory that treats only one electron at a time. While this might seem to be an absurd assumption, since electrons are charged and repel one another strongly, such single-electron theories often work remarkably well. Quantum mechanics is essential for understanding why this is so. All electrons are intrinsically identical to one another, just as are all protons, all neutrons, and so forth. Quantum mechanics sets very stringent rules for the behavior of systems containing many identical particles. If the positions of two identical particles are interchanged, quantum mechanics naturally insists that there be no observable consequence. Except in certain rare cases to be described below, there are only two ways in which the quantum wave function of the material can satisfy this requirement: either (1) nothing at all happens to the wave function upon interchange of two particles, or (2) it changes its sign. Particles for which the wave function changes sign are called fermions, while those for which the sign is preserved upon interchange are known as bosons.

Electrons are fermions, and thus a many-electron wave function changes sign when two are interchanged. This property underlies the Pauli exclusion principle, which high school chemistry students are usually told means that no two electrons can be in the same place at the same time. More precisely, two electrons are forbidden from occupying the same quantum state. Despite their vagueness, these statements make it easy to see why the Pauli principle has such vast significance for the theory of materials. If no two electrons can be in the same place at the same time, they rarely get so close together that their mutual repulsion is extremely strong. If no two can occupy the same quantum state, then at low temperatures the many electrons in a material are forced to sequentially occupy higher and higher energy levels, forming a “Fermi sea.” In some circumstances, interactions between electrons are not strong enough to disturb any but the relatively few levels that are near the surface of this sea. In effect, the Pauli principle converts what at first appears to be a hopelessly strongly interacting system into a more weakly interacting one. In a nutshell, this is why scientists understand the properties of simple metals as well as they do.

Remarkably, a more sophisticated version of the “Fermi liquid” picture just described often works very well even when the repulsive interactions between electrons are fairly strong (compared to the average kinetic energy of electrons). In these cases, the properties of the material can be described in terms of new entities, known as quasi-particles, which behave in much the same way as the original