The Mott-Ioffe-Regel limit and resistivity crossover in a tractable electron-phonon model

Abstract

Many metals display resistivity saturation - a substantial decrease in the slope of the resistivity as a function of temperature, that occurs when the electron scattering rate ${\tau }^{-1}$ becomes comparable to the Fermi energy $E_F/\hslash$ (the Mott-Ioffe-Regel limit). At such temperatures, the usual description of a metal in terms of ballistically propagating quasiparticles is no longer valid. We present a tractable model of a large $N$ number of electronic bands coupled to $N^2$ optical phonon modes, which displays a crossover behavior in the resistivity at temperatures where ${\tau }^{-1}\sim E_F/\hslash$. At low temperatures, the resistivity obeys the familiar linear form, while at high temperatures, the resistivity still increases linearly, but with a modified slope (that can be either lower or higher than the low-temperature slope, depending on the band structure). The high temperature non-Boltzmann regime is interpreted by considering the diffusion constant and the compressibility, both of which scale as the inverse square root of the temperature.

References in corpus (1)

• Theory of universal incoherent metallic transport

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