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 x 2 - y 2 symmetry condensate symmetry.