NMR and NQR fluctuation effects in layered superconductors

Abstract

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 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 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 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.

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