Volovik effect on NMR measurements of unconventional superconductors

Abstract

We studied the Volovik effect on the NMR measurements of the two unconventional superconducting (SC) states, the d-wave and $\pm$s-wave states. We showed the generic field dependencies of the spin-lattice relaxation rate $1/T_1$ and Knight shift $K$ at low temperature limit in the pure cases as: $1/T_1 \propto H \log H$, $K \propto \sqrt{H}$ for the d-wave, and $1/T_1 \propto H$, $K \propto H$ for the $\pm$s-wave state, respectively. Performing numerical calculations we showed that these generic power laws survive for the good part of low field region with the realistic amount of impurities. We also found that the Volovik effect acts as an equivalent pair breaker as the unitary impurity scattering, hence induces the same temperature evolutions on $1/T_1$ and $K$, respectively, as the unitary impurities in both SC states. This finding implies that the Volovik effect should always be taken into account for the analysis of the NMR measurements in the mixed state.