Electrical resistivity at large temperatures: Saturation and lack thereof

Abstract

Many transition metal compounds show a saturation of the electrical 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, 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-Tc cuprates, we use the f-sum rule. We demonstrate that the f-sum rule leads to a natural 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 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 Tc 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.

Colloquium: Saturation of electrical resistivity

“…Again, this suggests that as T is increased, the Drude peak disappears without the incoherent part changing very much. In the following, we therefore assume that T is so large that the Drude peak has disappeared (Calandra and Gunnarsson, 2002).…”

“…They also pointed out that higher order terms in (d/l) may be important. Calandra and Gunnarsson, 2002). The phonon frequency is ω ph = 0.1 eV.…”

Saturation of resistivity and Kohler's rule in Ni-dopedLa1.85Sr0.15CuO4cuprate

“…4(c) fails completely. Concluding, the signs of resistivity saturation both at the value ρ IRM and with n-dependence from Boltzmann theory reflect metallic-like character of transport despite small volume of Fermi surface and strong disorder in underdoped LSCO. A fully quantum-mechanical explanation of saturation is still lacking [26,46,[59][60][61]. Evidently however, strong electron-electron interactions [62] do not invalidate the ρ IRM limit [27].…”

Transport properties in correlated systems: An analytical model

“…10. In this analysis the resistivity saturation is achieved when the spread of the Drude peak is of the same order of the bandwidth W and the optical conductivity is described by a featureless structure up to the energy scale W .…”

“…Following Ref. 10, we relate the effective bandwidth to the lowest order momentum of the dispersion, in particular in the first casẽ…”