High Temperature Superconductivity in Strongly Correlated Electronic Systems

In this chapter we give a selective review of our work on the role of electron correlation in the theory of high-temperature superconductivity (HTSC). The question of how electronic repulsions might give rise to off-diagonal long-range order (ODLRO) in high-temperature superconductors is currently one of the key questions in the theory of condensed matter. This chapter argues that the key to understanding the occurrence of HTSC in cuprates is to be found in the Bohm-Pines Hamiltonian, modified to include a polarizable dielectric background. The approach uses reduced electronic density matrices and discusses how these can be used to understand whether ODLRO giving rise to superconductivity might arise from a Bohm-Pines-type potential which is comprised of a weak long-range attractive tail and a much stronger short-range repulsive Coulomb interaction. This allows time-reversed electron pairs to undergo a superconducting condensation on alternant cuprate lattices. Thus, a detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time-reversed pairs of electrons effectively avoid the repulsive hard-core of the interelectronic Coulomb interaction but reside on average in the attractive well of the effective potential. In a superconductor the plasma wave function becomes the longitudinal component of a massive photon by the Anderson-Higgs mechanism. The alternant cuprate lattice structure is the key to achieving HTSC in cuprates with d(x2) - (y2) symmetry condensate symmetry