Influence of internal disorder on the superconducting state in the organic layered superconductor $\kappa -(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}-\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{Cu}[\mathrm{N}\left(\mathrm{CN}{)}_2\right]\mathrm{Br}$

We report high-sensitivity ac susceptibility measurements of the penetration depth in the Meissner state of the layered organic superconductor $\kappa -(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}-\mathrm{T}\mathrm{T}\mathrm{F}{)}_2\mathrm{Cu}[\mathrm{N}\left(\mathrm{CN}{)}_2\right]\mathrm{Br}.$ We have studied nominally pure single crystals from the two different syntheses and employed controlled cooling procedures in order to minimize intrinsic remnant disorder at low temperatures associated with the glass transition, caused by ordering of the ethylene moieties in BEDT-TTF molecule at $T_{\mathrm{G}}=75\mathrm{}\mathrm{K}.$ We find that the optimal cooling procedures (slow cooling of $-0.2\mathrm{K}/\mathrm{h}$ or annealing for 3 days in the region of $T_{\mathrm{G}})$ needed to establish the ground state depend critically on the sample origin, indicating different relaxation times of terminal ethylene groups. We show that, in the ground state, the behavior observed for nominally pure single crystals from both syntheses is consistent with unconventional d-wave order parameter. The in-plane penetration depth ${\lambda }_{\mathrm{in}}\mathrm{}\left(T\right)\mathrm{}$ is strongly linear, whereas the out-of-plane component ${\lambda }_{\mathrm{out}}\mathrm{}\left(T\right)\mathrm{}$ varies as $T^2.$ In contrast, the behavior of single crystals with long relaxation times observed after slow $(-0.2\mathrm{K}/\mathrm{h})$ cooling is as expected for a d-wave superconductor with impurities [i.e., ${\lambda }_{\mathrm{in}}\mathrm{}\left(T\right)\mathrm{}\propto {\lambda }_{\mathrm{out}}\mathrm{}\left(T\right)\mathrm{}\propto T^2]$ or might be also reasonably well described by the s-wave model. Our results might reconcile the contradictory findings previously reported by different authors.