Ioffe-Regel criterion and resistivity of metals

Abstract

Resistivity saturation is a general phenomenon observed in metals whose electrons have short mean free paths. The approach to saturation can be described rather well by the parallel-resistor formula $\frac{1}{\rho }=\frac{1}{{\rho }_{\mathrm{ideal}}}+\frac{1}{{\rho }_{\mathrm{sat}}}$, where ${\rho }_{\mathrm{ideal}}$ is calculated by the usual theory and ${\rho }_{\mathrm{sat}}$ represents a constant "shunt" resistor. In this work it is shown that the requirement of the minimum time between collisions (Ioffe-Regel criterion), incorporated in the distribution of free times, leads to the parallel-resistor formula.