Negative intercept of the apparent zero-temperature extrapolated linear-in-$T$ metallic resistivity

TL;DR

This paper analyzes how naive extrapolation of high-temperature linear resistivity in metals can lead to an unphysical negative resistivity at zero temperature, emphasizing the importance of the temperature regime used for extrapolation.

Contribution

It provides a theoretical framework linking the negative intercept in resistivity extrapolation to the temperature dependence of the linear-in-$T$ resistivity slope.

Findings

Negative extrapolated resistivity depends on the extrapolation temperature range.

Correct zero resistivity at $T=0$ is achieved only when extrapolating from $T \,\gg T_D$.

The relationship between the negative intercept and the resistivity slope is established.

Abstract

We consider the well-known phonon scattering induced high-temperature linear-in-$T$ metallic resistivity, showing that a naive extrapolation of the effective linearity from high temperatures to $T=0$ leads to an apparent zero-temperature negative resistivity. The precise magnitude of this extrapolated $T=0$ negative resistivity depends on the temperature regime from where the extrapolation is carried out, and approaches the correct physical result of zero resistivity at $T=0$ only if the extrapolation starts from $T\gg T_D$, where $T_D$ is the Debye temperature. We establish a theoretical relationship between the negative intercept and the slope of the linear-in-$T$ resistivity as a function of the temperature $T$ from where the extrapolation is carried out. Experimental implications of our finding are discussed for the much-discussed Planckian behavior of the transport scattering rate.