A statistical model for the intrinsically broad superconducting to normal transition in quasi-two-dimensional crystalline organic metals

Although quasi-two-dimensional organic superconductors such as $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ seem to be very clean systems, with apparent quasiparticle mean-free paths of several thousand \AA, the superconducting transition is intrinsically broad (e.g $\sim 1$ K wide for $T_c \approx 10$ K). We propose that this is due to the extreme anisotropy of these materials, which greatly exacerbates the statistical effects of spatial variations in the potential experienced by the quasiparticles. Using a statistical model, we are able to account for the experimental observations. A parameter $\bar{x}$, which characterises the spatial potential variations, may be derived from Shubnikov-de Haas oscillation experiments. Using this value, we are able to predict a transition width which is in good agreement with that observed in MHz penetration-depth measurements on the same sample.