Eliashberg theory of the superconducting state of marginal Fermi liquids

Abstract

The marginal Fermi liquid (MFL) which describes the anomalous normal state of the cuprates is extended to a d-wave superconductive state. A phenomenological collective excitation, P-0 (omega, T), is taken such that it gives rise to, after renormalization, the MFL behavior in the normal state. With the P-0, the renormalized excitation spectrum and pairing function in superconductive state are calculated self-consistently within the Eliashberg formalism. In the superconductive state, the self-energy deviates from the normal state MFL omega/T-scaling and develops a new energy scale of omega(0) approximate to 2Delta, where Delta is the pairing amplitude.