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We give a theoretical analysis of published experimental studies of theeffects of impurities and disorder on the superconducting transitiontemperature, T_c, of the organic molecular crystals kappa-ET_2X and beta-ET_2X(where ET is bis(ethylenedithio)tetrathiafulvalene and X is an anion eg I_3).The Abrikosov-Gorkov (AG) formula describes the suppression of T_c both bymagnetic impurities in singlet superconductors, including s-wavesuperconductors and by non-magnetic impurities in a non-s-wave superconductor.We show that various sources of disorder lead to the suppression of T_c asdescribed by the AG formula. This is confirmed by the excellent fit to thedata, the fact that these materials are in the clean limit and the excellentagreement between the value of the interlayer hopping integral, t_perp,calculated from this fit and the value of t_perp found from angular-dependantmagnetoresistance and quantum oscillation experiments. If the disorder is, asseems most likely, non-magnetic then the pairing state cannot be s-wave. Weshow that the cooling rate dependence of the magnetisation is inconsistent withparamagnetic impurities. Triplet pairing is ruled out by several experiments.If the disorder is non-magnetic then this implies that l>=2, in which caseOccam's razor suggests that d-wave pairing is realised. Given the proximity ofthese materials to an antiferromagnetic Mott transition, it is possible thatthe disorder leads to the formation of local magnetic moments via some novelmechanism. Thus we conclude that either kappa-ET_2X and beta-ET_2X are d-wavesuperconductors or else they display a novel mechanism for the formation oflocalised moments. We suggest systematic experiments to differentiate betweenthese scenarios.Comment: 18 pages, 5 figure

physical review. b, condensed matter and materials physics

Dependence of the superconducting transition temperature of organic molecular crystals on intrinsically nonmagnetic disorder: A signature of either unconventional superconductivity or the atypical formation of magnetic moments