The suppression of superconductivity by nonmagnetic disorder is investigated systematically in the organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$. We introduce a nonmagnetic disorder arising from molecule substitution in part with deuterated BEDT-TTF or BMDT-TTF for BEDT-TTF molecules and molecular defects introduced by X-ray irradiation. A quantitative evaluation of the scattering time $\tau_{ \rm dHvA}$ is carried out by de Haas-van Alphen (dHvA) effect measurement. A large reduction in $T_{ \rm c}$ with a linear dependence on $1/\tau_{ \rm dHvA}$ is found in the small-disorder region below $1/\tau_{ \rm dHvA} \simeq$ 1 $\times$ 10$^{ 12}$ s$^{ -1}$ in both the BMDT-TTF molecule-substituted and X-ray-irradiated samples. The observed linear relation between $T_{ \rm c}$ and $1/\tau_{ \rm dHvA}$ is in agreement with the Abrikosov-Gorkov (AG) formula, at least in the small-disorder region. This observation is reasonably consistent with the unconventional superconductivity proposed thus far for the present organic superconductor. A deviation from the AG formula, however, is observed in the large-disorder region above $1/\tau_{ \rm dHvA} \simeq$ 1 $\times$ 10$^{ 12}$ s$^{ -1}$, which reproduces the previous transport study (J. G. Analytis { \it et al.}: Phys. Rev. Lett. { \bf 96} (2006) 177002). We present some interpretations of this deviation from the viewpoints of superconductivity and the inherent difficulties in the evaluation of scattering time.
Categories: cond-mat.supr-con cond-mat.str-el