Phenomenology of the superconductive state of a marginal Fermi liquid

We consider an extension of the marginal-Fermi-liquid model to the s-wave superconducting state by phenomenologically incorporating the superconducting gap into the scattering spectrum. The linear-in-temperature scattering rate due to the high density of low-energy electronic excitations naturally leads to a large pair-breaking rate, which suppresses Tc. Below Tc the low-energy excitations are self-consistently suppressed due to the opening of a superconducting gap. This leads to a vanishing of both the inelastic-scattering rate and pair breaking below Tc. There are a number of consequences not found in traditional BCS electron-phonon--induced s-wave superconductors. For energies below 3{Δ}, the quasiparticles become well defined in the superconducting state, while they are marginal (scattering rate proportional to the energy) in the normal state. This produces a two-peaked structure in the one-particle spectra---a sharp feature between {Δ} and 3{Δ} (depending on momentum) and a broad hump with an onset at 3{Δ} (independent of momentum). The transport properties do not obey the usual BCS rules. Transport properties in the q{→}0 limit and for low frequencies {ω}{}{Δ} show peaks below Tc. These are observable in microwave conductivity and in electronic thermal conductivity. Local or momentum-averaged response properties such as the nuclear relaxation rate show no peak, but a sharp drop below Tc. The superconductive gap opens very rapidly below Tc, and the value of 2{Δ}/Tc can cover a wide range, depending on parameters. The physical origin of these results is discussed, and comparison to experiment is made.