In a semi-classical theory, the resistivity in a metal can be interpreted in terms of the mean free path l, the average distance an electron travels before it is scattered. For a good metal, l is typically very much larger than the distance d between two atoms. For some systems, e.g., some transition metal compounds, it is found that l and d can become comparable. Many such compounds were studied in the 70's and 80's, and it was found that the resistivity saturated when l became comparable to d. This behaviour was therefor considered as universal. As an example, the resistivity of Nb3Sn and Cu are compared in a postscript file. The resistivity corresponding to l=d (Ioffe-Regel) is also shown. Later some apparent exceptions were found, e.g., i) some high temperature superconductors and ii) the alkali-doped fullerenes (A3C60)( see postscript file). These systems could, however, be in exotic states, where only a small fraction of the nominal conduction electrons actually contribute to the conductivity. In that case one would have to conclude that l is correspondingly larger, and perhaps even larger than d.
Our aim has therefore been to construct a microscopic model of the alkali-doped fullerenes and then to solve this model essentially exactly by using a quantum Monte-Carlo method. If such a model shows a resistivity which becomes so large that l is much smaller than d (the separation between two fullerene molecules), this would then provide a counter example to the assumed universality of the resistivity saturation when l is similar to d.
We find that a model including the sattering of the electrons from the intramolecular phonons indeed has such a behavior Nature 405 , 1027 (2000) . This illustrates that saturation when l and d are comparable is not a universal phenomenon, since it would then also have to happen in our model. A general discussion is also given by P.B. Allen in "Misbehaviour in metals", News and Views, Nature 405 , 1007 (2000).