A model of marginal Fermi liquid in d-wave superconductive state

Abstract

The marginal Fermi liquid (MFL) phenomenology of the cuprates in a normal state is extended to a d-wave superconductive state. We assume that the MFL collective excitation can be factored into a “bare excitation,” P 0( ω, T), and the susceptibility, χ( ω, T), such that the P 0( ω, T) gives rise to, after renormalization, the MFL behavior in the normal state: Im P n( ω, T) ∝ −tanh( ω/2 T). With the P 0 determined this way at a given temperature T, the superconductivity (SC) is incorporated by including the pairing processes in addition to normal ones in the electronic susceptibility. The renormalized excitation spectrum in a SC state is calculated self-consistently together with the renormalization function Z( ω) and pairing function Δ( ω) within the Eliashberg formalism. The following distinctive features of the SC emerging from a MFL, compared with that from a Fermi liquid, are found: (a) the pairing function Δ( ω) of MFL SC does not show any particular bosonic energy scale, and there exist substantial damping and suppression of Δ( ω) in the small frequency region, (b) the renormalized excitation spectrum gets suppressed below ω 0≈2 Δ and shows a hump around ω 0, and (c) the self-energy deviates from the MFL ω/ T-scaling in superconductive state.