Correlated quantum fluids and the search for a new theory of metals

One of the key discoveries at the close of the last century was that of the electron (Nobel prize 1906). As well as heralding the dawn of particle physics, it also gave a fundamental basis for understanding electrical conduction in solids. As this century closes, we are discovering new materials in which the interactions between electrons can lead to a quantum fluid where the electron no longer appears to be the fundamental current-carrying entity. Notable examples are the high-temperature cuprate superconductors, heavy-fermion compounds and semiconductors in the quantum Hall regime. Here we review why a radical revision of our understanding of the electron quantum fluid is needed. A common thread is the possibility of exotic quantum phases of matter arising from strong electron correlations, reduced dimensionality, and the competition between magnetism and electronic conduction.