Physics Colloquium

It is now just over twenty years since Bednorz and Müller discovered high-temperature superconductivity in La2-xBaxCuO4. Despite a considerable expenditure of brain power, we are still not close to a theoretical consensus on why layered copper-oxide compounds are superconducting. The problem is especially challenging (and exciting) because standard models break down for these materials. The Bardeen-Cooper-Schrieffer theory of superconductivity, which is celebrating its 50th anniversary this year, is built on top of Fermi liquid theory, whose assumptions are not valid for the cuprates. One must instead deal with the underlying and unresolved problem of the transformation, with electronic doping, from a correlated insulator to a metal (the Mott transition). While the theoretical picture remains controversial, the experimental picture has gradually become much clearer. I will present a perspective on the cuprates obtained from experimental techniques such as neutron scattering, photoemission, optical conductivity, and scanning tunneling spectroscopy. I will also show that most of the observed properties are compatible with the existence of stripes---spatial inhomogeneities of the charge and spin densities that are not included in conventional theory.