<i>Colloquium</i>: Saturation of electrical resistivity

TLDR

Resistivity saturation occurs in many metallic systems when resistivity reaches a critical value, after which its temperature dependence is markedly reduced, typically because the mean free path approaches interatomic distances (the Ioffe–Regel condition). The authors review experimental observations and early theories of resistivity saturation, then discuss recent theoretical work that examines both compliance with and violations of the Ioffe–Regel condition. They demonstrate how the semiclassical Ioffe–Regel condition can be derived quantum‑mechanically under specific assumptions, and explain why these assumptions break down in high‑Tc cuprates and alkali‑doped fullerides. Recent studies have identified several exceptions to the Ioffe–Regel rule.

Abstract

Resistivity saturation is observed in many metallic systems with a large resistivity, i.e., when the resistivity has reached a critical value, its further increase with temperature is substantially reduced. This typically happens when the apparent mean free path is comparable to the interatomic separations - the Ioffe-Regel condition. Recently, several exceptions to this rule have been found. Here, we review experimental results and early theories of resistivity saturation. We then describe more recent theoretical work, addressing cases both where the Ioffe-Regel condition is satisfied and where it is violated. In particular we show how the (semiclassical) Ioffe-Regel condition can be derived quantum-mechanically under certain assumptions about the system and why these assumptions are violated for high-Tc cuprates and alkali-doped fullerides.