Suppression of superconductivity by non-magnetic disorder in organic superconductor $\kappa$-(BEDT-TTF)${}_2$Cu(NCS)${}_2$

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 ${\tau }_{\mathrm{d}\mathrm{H}\mathrm{v}\mathrm{A}}$ is carried out by de Haas-van Alphen (dHvA) effect measurement. A large reduction in $T_{\rm c}$withalineardependenceon$1/\tau_{\rm dHvA}$ is found in the small-disorder region below $1\mathrm{/}{\tau }_{\mathrm{d}\mathrm{H}\mathrm{v}\mathrm{A}}\simeq$ 1 $\times$ 10${}^{12}$ s${}^{-1}$ in both the BMDT-TTF molecule-substituted and X-ray-irradiated samples. The observed linear relation between $T_{\mathrm{c}}$ 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 $1\mathrm{/}{\tau }_{\mathrm{d}\mathrm{H}\mathrm{v}\mathrm{A}}\simeq$ 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.