Effects of strong magnetic fields on pairing fluctuations in high-temperature superconductors

We present the theory for the effects of superconducting pairing fluctuations on the nuclear spin-lattice relaxation rate ${1/T}_1$ and the NMR Knight shift for layered superconductors in high magnetic fields. These results can be used to clarify the origin of the pseudogap in high-$T_c$ cuprates, which has been attributed to spin fluctuations as well as pairing fluctuations. We present theoretical results for $s$-wave and $d$-wave pairing fluctuations and show that recent experiments in optimally doped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ are described by $d$-wave pairing fluctuations [V. F. Mitrović et al., Phys. Rev. Lett. 82, 2784 (1999); H. N. Bachman et al. (unpublished)]. In addition, we show that the orthorhombic distortion in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ accounts for an experimentally observed discrepancy between ${1/T}_1$ obtained by nuclear quadrupole resonance and nuclear magnetic resonance at low field. We propose an NMR experiment to distinguish a fluctuating $s$-wave order parameter from a fluctuating strongly anisotropic order parameter, which may be applied to the system ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_{4\mathrm{-}\mathrm{\delta }}$ and possibly other layered superconductors.