The origin of the difference in the superconducting critical temperatures of the beta_H and beta_L phases of (BEDT-TTF)_2I_3

Incommensurate lattice fluctuations are present in the beta_L phase (T_c = 1.5 K) of ET_2I_3 (where ET is BEDT-TTF - bis(ethylenedithio)tetrathiafulvalene) but are absent in the beta_H phase (T_c = 7 K). We propose that the disorder in the conformational degrees of freedom of the terminal ethylene groups of the ET molecules, which is required to stabilise the lattice fluctuations, increases the quasiparticle scattering rate and that this leads to the observed difference in the superconducting critical temperatures, T_c, of the two phases. We calculate the dependence of T_c on the interlayer residual resistivity. Our theory has no free parameters. Our predictions are shown to be consistent with experiment. We describe experiments to conclusively test our hypothesis.