Electrical resistivity at large temperatures: Saturation and lack thereof

TL;DR

This paper models resistivity saturation in transition metal compounds and alkali-doped fullerenes, analyzing the conditions under which saturation occurs or is absent, using the f-sum rule and considering electron interactions and phonon effects.

Contribution

It introduces models explaining resistivity saturation and lack thereof, applying the f-sum rule to different systems with varying electron interactions and phonon couplings.

Findings

Transition metal compounds show resistivity saturation consistent with the Ioffe-Regel limit.

High-Tc cuprates do not violate the saturation limit, aligning with experimental data.

Alkali-doped fullerenes exhibit rapid resistivity growth post-saturation, making the concept less meaningful.

Abstract

Many transition metal compounds show saturation of the resistivity at high temperatures, T, while the alkali-doped fullerenes and the high-Tc cuprates are usually considered to show no saturation. We present a model of transition metal compounds, showing saturation, and a model of alkali-doped fullerenes, showing no saturation. To analyze the results we use the f-sum rule, which leads to an approximate upper limit for the resistivity at large T. For some systems and at low T, the resistivity increases so rapidly that this upper limit is approached for experimental T. The resistivity then saturates. For a model of transition metal compounds with weakly interacting electrons, the upper limit corresponds to a mean free path consistent with the Ioffe-Regel condition. For a model of the high Tc cuprates with strongly interacting electrons, however, the upper limit is much larger than the Ioffe-Regel condition suggests. Since this limit is not exceeded by experimental data, the data are consistent with saturation also for the cuprates. After "saturation" the resistivity usually grows slowly. For the alkali-doped fullerenes, "saturation" can be considered to have happened already for T=0, due to orientational disorder. For these systems, however, the resistivity grows so rapidly after "saturation" that this concept is meaningless. This is due to the small band width and to the coupling to the level energies of the important phonons.