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 T(c). Below T(c) 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 T(c). There are a number of consequences not found in traditional BCS electron-phonon-induced s-wave superconductors. For energies below 3-DELTA, 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 DELTA and 3-DELTA (depending on momentum) and a broad hump with an onset at 3-DELTA (independent of momentum). The transport properties do not obey the usual BCS rules. Transport properties in the q-->0 limit and for low frequencies-omega << DELTA show peaks below T(c). 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 T(c). The superconductive gap opens very rapidly below T(c), and the value of 2-DELTA/T(c) can cover a wide range, depending on parameters. The physical origin of these results is discussed, and comparison to experiment is made.