Eliashberg Theory of the Superconducting State of Marginal Fermi Liquids

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, P0(ω,T), is taken such that it gives rise to, after renormalization, the MFL behavior in the normal state. With the P0, 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 ω/T-scaling and develops a new energy scale of ω0≈2Δ, where Δ is the pairing amplitude.