Nuclear spin relaxation rate of disorderedpx+ipy-wave superconductors

Abstract

Based on an effective Hamiltonian with the binary alloy disorder model defined in the triangular lattice, the impurity scattering effects on the density of states and especially on the spin-lattice relaxation rate $1∕{T}_{1}$ of ${p}_{x}+i{p}_{y}$-wave superconductors are studied by solving numerically the Bogoliubov--de Gennes equations. In the clean limit, the coherence peak of $1∕{T}_{1}$ is observed as expected. More intriguingly, for strong scattering potential, the temperature dependence of $1∕{T}_{1}$ exhibits the two different power-law behaviors near ${T}_{\mathrm{c}}$ and at low temperatures, respectively, which is qualitatively consistent with the nuclear quadrupolar resonance measurement of the newly discovered superconductor ${\mathrm{Na}}_{x}\mathrm{Co}{\mathrm{O}}_{2}∙y{\mathrm{H}}_{2}\mathrm{O}$ $(x=0.35)$. We argue that the disorder effect plays an important role in the thermodynamic properties of the ${p}_{x}+i{p}_{y}$-wave pairing state as indicated in this paper, as well as other superconducting states with unconventional pairing symmetries. Therefore further experimental exploration is expected to determine the actual pairing symmetry of this material.