Anisotropics-wave gap and nuclear magnetic resonance in high-temperature superconductors

The Knight shift and the nuclear magnetic relaxation rates ${\mathit{W}}_{\mathrm{\perp }}^{63}$, ${\mathit{W}}_{\mathrm{\parallel }}^{63}$, and ${\mathit{W}}_{\mathrm{\parallel }}^{17}$ are calculated for temperatures below the superconducting transition temperature of the high-temperature cuprate superconductors; the superscripts refer to the ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ and the ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ nuclei while the subscripts refer to the direction of the magnetic field with respect to the CuO layers. The calculations are based on a recently proposed interlayer tunneling mechanism of superconductivity in these materials. In general, the results are consistent with experiments even though the superconducting gap respects the full point-group symmetry of the lattice (anisotropic s wave); the anisotropy of the magnitude of the gap is an essential element.