Electronic structure of doped insulators and high temperature superconductivity

The Fermi liquid theory of the normal state and the BCS-Eliashberg theory o f the superconducting state were designed for good metals not for doped ant iferromagnetic insulators, such as the high temperature superconductors. Co nsequently, it is necessary to understand the electronic structure of the d oped insulator and to develop a new mechanism and many-body theory of super conductivity for these materials. It will be argued that, since the motion of a single hole in an antiferromagnet is frustrated, the driving force for the physics of a finite concentration of doped holes is the need to reduce their zero-point kinetic energy. This proceeds in. three steps that are re flected in a sequence of crossovers and phase transitions. First of all, th e system forms a charge-inhomogeneous state - an electronic liquid crystal phase, involving an array of metallic stripes, which lowers the kinetic ene rgy along a stripe. lit the direction perpendicular to the stripes, the kin etic energy is lowered by pair hopping, which proceeds in two steps. Local pair hopping induces spin. pairing and then, cat a lower temperature, pair hopping from stripe to stripe produces superconducting phase coherence. Som e of the experimental support for the various aspects of this model will be described.