Universality of the Mott–Ioffe–Regel limit in metals

Abstract

The absence of resistivity saturation in many strongly correlated metals, including the high-temperature superconductors, is critically examined from the viewpoint of optical conductivity measurements. Coherent quasiparticle conductivity, in the form of a Drude peak centred at zero frequency, is found to disappear as the mean free path (at ω = 0) becomes comparable with the interatomic spacing. This basic loss of coherence at the so-called Mott–Ioffe–Regel (MIR) limit suggests that the universality of the MIR criterion is preserved even in the presence of strong electron correlations. We argue that the shedding of spectral weight at low frequencies, induced by strong correlation effects, is the primary origin of the extended positive slope of the resistivity to high temperatures observed in all so-called ‘bad metals’. Moreover, in common with those metals which exhibit resistivity saturation at high temperatures, the scattering rate itself, as extracted from optical spectra, saturates at a value consistent with the MIR limit. We consider possible implications that this ceiling in the scattering rate may have for our understanding of transport within a wide variety of bad metals and suggest a better method for analysing their optical response.

Acknowledgements

The authors would like to acknowledge fruitful discussions with N. Bontemps, A. J. Schofield, T. W. Silk, T. Timusk, D. van der Marel, J. A. Wilson, Y. Yanase and J. Zaanen. We also thank J. A. Wilson for his critical reading of the manuscript and J. C. Alexander for preparing figure 2.

Notes

†Note that, in the model of this paper, the PRF is expressed in terms of conductivities, that is σ_Drude(T, ω) + σ_min, rather than as here, where it applies to the scattering rates (2).

†Strictly speaking, the critical sum rule shown in equation (10) is a partial sum rule, crossing over to the total sum rule for W→ ∞.