Fermi-liquid damping and NMR relaxation in superconductors

Electron collisions for a two-dimensional Fermi-liquid (FL) are shown to give a quasiparticle damping with interesting frequency and temperature variations in the BCS superconducting state. The spin susceptibility which determines the structure of the damping is analyzed in the normal state for a Hubbard model with a constant on-site Coulomb repulsion. This is then generalized to the superconducting state by including coherence factors and self-energy and vertex corrections. Calculations of the NMR relaxation rate reveal that the FL damping structure can reduce the Hebel-Slichter peak, in agreement with data on the organic superconductor (MDT-TTF)₂{AuI}₂$ (methylenedithiotetrathiafulvalene salt). However, the strongly suppressed FL damping in the superconducting state does not eliminate the Hebel-Slichter peak, and thus suggests that other mechanisms are needed to explain the NMR data on (TMTSF)₂{ClO}₄$ (bistetramethyltetraselenafulvaleneperchlorate), the BEDT organic compounds, and cuprate superconductors. Predictions of the temperature variation of the damping and the spin response are given over a wide frequency range as a guide to experimental probes of the symmetry of the superconducting pairs. {} 1996 The American Physical Society.