High-temperature superconductivity in cuprates and organics : where do we stand ? (1)

The most resounding successes of solid-state physics rest on two pillars: band theory and the BCS theory of phonon-mediated superconductivity. Nevertheless, these theories have failed to explain the normal and superconducting phases of cuprates and organic layered superconductors. In this first lesson, I first identify the theoretical difficulties suggested by the structure and phase diagrams of these materials. I discuss observations that demonstrate that an interaction-induced metal-insulator transition (the so-called Mott transition) controls the physics. I then present Hubbard's single-band model and demonstrate that it explains not only the antiferromagnetism observed in these compounds, but also the spectral weight transfer. This leads to a better definition of what a phase of matter is, and why there are differences between weak and strong correlations in antiferromagnetic and superconducting phases. After a brief review of theoretical methods, I turn to the question of phase diagrams in greater detail. What are the three main classes of pseudogap mechanisms? Why are there two domes in the cuprate phase diagram? What do theoretical methods explain, at least qualitatively? I conclude with a few brief comments on heavy fermions and the role of quantum critical points for superconductivity.