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 T_C. 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 T₁^-1 for a clean s-wave superconductor, with and without pair breaking effects, using the static pair fluctuation propagator D. The increase in T₁^-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 T₁^-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 T₁^-1 and on the transverse relaxation rate T₂^-1 on both sides of the BKT transition temperature T_BKT<T_C. 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 discuss the relaxation rates for real multilayer systems where D can be small and thus increase the lifetime of a VA pair, leading to an enhancement of the rates. We also discuss in some detail the experimental feasibility of observing the effects of amplitude fluctuations in layered s-wave superconductors such as the dichalcogenides and the effects of phase fluctuations in s- or d-wave superconductors such as the layered cuprates.