Electrical resistivity at large temperatures: Saturation and lack thereof

Many transition metal compounds show a saturation of the electrical resistivity at high temperatures T while the alkali-doped fullerenes and the high-T-c cuprates are usually considered to show no saturation. We present a model of transition metal compounds, which shows saturation, and a model of alkali-doped fullerenes, which shows no saturation. The electron scattering is assumed to be due to interaction with phonons. The properties of these models are determined by performing quantum Monte Carlo calculations. To analyze the results, as well as earlier results for the high-T-c cuprates, we use the f-sum rule. We demonstrate that the f-sum rule leads to a natural upper limit for the resistivity, which usually has a weak T dependence. For some systems and at low T, the resistivity increases so rapidly that this upper limit is approached for experimentally accessible temperatures. The resistivity then saturates. For a model of transition metal compounds with weakly interacting electrons, the upper limit corresponds to an apparent mean free path consistent with the Ioffe-Regel condition. For a model of the high-T-c cuprates with strongly interacting electrons, however, the upper limit is much larger than the Ioffe-Regel condition suggests. This upper limit is not exceeded by experimental resistivities. The experimental data for the cuprates are therefore consistent with saturation. After saturation the resistivity normally grows slowly. The alkali-doped fullerenes can be considered as systems where saturation has happened already for T=0, due to orientational disorder. We show, however, that for these systems the resistivity grows so rapidly after "saturation" that this concept is meaningless. This is due both to the small band width and to the coupling to the level energies of the important (intramolecular) phonons in the fullerenes.