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

TL;DR

This paper introduces a solvable electron-phonon model that captures the resistivity crossover at the Mott-Ioffe-Regel limit, showing how resistivity behavior changes from low to high temperatures in metals.

Contribution

A tractable large-N model is developed to study resistivity saturation and crossover phenomena in metals near the Mott-Ioffe-Regel limit.

Findings

Resistivity exhibits a crossover from linear to modified linear behavior at high temperatures.

High-temperature resistivity scales with the inverse square root of temperature.

The model explains resistivity saturation without quasiparticle breakdown.

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 $E_F/\hbar$ (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 At such temperatures, the usual description of a metal in terms of ballistically propagating quasiparticles is no longer valid.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 $\tau^{-1}\sim E_F/\hbar$. 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.