Relieving the Frustration:
High T_c Superconductivity in Doped Antiferromagnets

The standard theory of metals, and of the Fermi surface instabilities that produce low temperture ordered states in metals (of which BCS theory is the most notable and successful example) are all based on the idea that the electron kinetic energy dominates the physics, and that interaction effects can be treated as an afterthought. The normal state is thus, essentially, the ground-state of the kinetic energy, and the instabilities are "potential" driven. In highly correlated materials, and especially in doped antiferromagnets (or more generally, doped Mott insulators) the short-range piece of the electron-electron repulsion is the dominant energy, which means that the kinentic energy is strongly frustrated so the normal state is not a Fermi liquid, and any order that develops on cooling tends to be "kinetic energy driven." From this viewpoint, the various transitions and crossovers that have been observed in the most studied example of a doped antiferromagnet, the high temperature superconductors, can be understood as successive levels of self-organization whereby the zero-point kinetic energy is minimized: a) Local and global charge "stripe" order is a manifestation of Coulomb frustrated kinetic phase separation, whereby locally metallic regions are created in the insulating matrix. b) Pseudo-gap formation, which plays the role of superconducting pairing in conventional superconductors, is driven virtual tunnelling of pairs from the metallic stripe regions into their immediate environement, a mechanism which we have named "the spin-gap proximity effect". c) Superconducting long-range order is triggered by phase ordering, whereby the superconducting pairs delocalize between stripes.