NMR and NQR Fluctuation Effects in Layered Superconductors

We study the effect of thermal fluctuations of the s-wave order parameter of a quasi two dimensional superconductor on the nuclear spin relaxation rate near the transition temperature TC . We consider both the effects of the amplitude fluctuations and the Berezinskii-Kosterlitz-Thouless (BKT) phase fluctuations in weakly coupled layered superconductors. In the treatment of the amplitude fluctuations we employ the Gaussian approximation and evaluate the longitudinal relaxation rate T−1 1 for a clean s-wave superconductor, with and without pair breaking effects, using the static pair fluctuation propagator D. The increase in T−1 1 due to pair breaking in D is overcompensated by the decrease arising from the single particle Green’s functions. The result is a strong effect on T−1 1 for even a small amount of pair breaking. The phase fluctuations are described in terms of dynamical BKT excitations in the form of pancake vortex-antivortex (VA) pairs. We calculate the effect of the magnetic field fluctuations caused by the translational motion of VA excitations on T−1 1 and on the transverse relaxation rate T −1 2 on both sides of the BKT transition temperature TBKT < TC . The results for the NQR relaxation rates depend strongly on the diffusion constant D that governs the motion of free and bound vortices as well as the annihilation of VA pairs. We