The origin of the difference in the superconducting critical temperatures of the betaₕ and betaₗ phases of (BEDT-TTF)₂I₃

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Incommensurate lattice fluctuations are present in the betaₗ phase (Tc = 1.5 K) of ET₂I₃ (where ET is BEDT-TTF - bis(ethylenedithio)tetrathiafulvalene) but are absent in the betaₕ phase (Tc = 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, Tc, of the two phases. We calculate the dependence of Tc 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.