Superconductivity in the presence of strong correlations and spin-orbit interactions

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Much of what we understand about simple metals and semiconductors is based on a single-particle picture. Once we determine what one electron does, then any macroscopic current or response is determined by this single-particle behaviour, with slight modifications to account for the statistics of the many electrons. In recent decades, however, researchers have discovered more and more materials that support conduction --- that is, they show metallic behaviour, and turn out to have extremely interesting properties. By way of example, a class of the high temperature cuprate materials, epitomized by La