Nuclear magnetic relaxation rate in a noncentrosymmetric superconductor

Noncentrosymmetric superconductors possess, in general, order parameters of mixed parity, i.e., the Cooper pairing state consists of spin-singlet and spin-triplet pairing components. We show that this property has important implications for the NMR and other measurable quantities in the heavy Fermion superconductor ${\mathrm{CePt}}_3\mathrm{Si}$. The aspect of parity mixing explains the apparently contradicting observations of a Hebel-Slichter peak in the nuclear spin-lattice relaxation rate $T_1^{-1}$ and the presence of power law in the low-temperature behavior of certain physical quantities, indicating line nodes in the quasiparticle gap.

Figure 1

The temperature dependence of the order parameters in units of $T_{\mathrm{c}}$. The spin-triplet component $\Delta$ (solid line) and the spin-singlet $s$-wave component $\Psi$ (dashed line). ${\omega }_{\mathrm{c}}=20T_{\mathrm{c}}$, ${\lambda }_m=0.12$, and $\nu =0.5$. Both $\Delta$ and $\Psi$ are real and positive.

Figure 2

Temperature dependence of the nuclear spin-lattice relaxation rate $1∕T_{1}T$ (solid lines), $\eta ={10}^{-4}{T}_{\mathrm{c}}$. (a) Dashed line is the contribution of the anomalous Green’s functions $W_{FF}$ related to the coherence effect. Dashed-dotted line is the contribution of the regular Green’s functions $W_{GG}$ related to the density of states. (b) Plot of the same data on a double-logarithmic scale. Dotted line is a plot of $T^2$. From the plot, it is noted that $T_1^{-1}$ follows the $T^3$ law at low temperatures.

Figure 3

Schematic figures of the gap structure on the Fermi surface. (a) Cross section of the Fermi surface, showing the places of gap nodes at which the gap $\mid \mathrm{\Psi }-\Delta \sin \theta \mid =0$. (b) Line nodes of the gap in the three-dimensional $\mathit{k}$ space.