Non-quasiparticle transport and resistivity saturation: A view from the large-N limit

TL;DR

This paper presents an exactly solvable large-N electron-phonon model demonstrating resistivity saturation at high temperatures due to a second conduction channel, challenging traditional quasiparticle-based explanations.

Contribution

It introduces the first analytically tractable model showing resistivity saturation arising from non-quasiparticle electron dynamics at high temperatures.

Findings

Resistivity saturates to a quantum-scale value at high T.

Saturation results from a second conduction channel, not limited electron lifetime.

Model aligns with the phenomenological parallel resistor formula.

Abstract

The electron dynamics in metals are usually well described by the semiclassical approximation for long-lived quasiparticles. However, in some metals, the scattering rate of the electrons at elevated temperatures becomes comparable to the Fermi energy; then, this approximation breaks down, and the full quantum-mechanical nature of the electrons must be considered. In this work, we study a solvable, large-$N$ electron-phonon model, which at high temperatures enters the non-quasiparticle regime. In this regime, the model exhibits "resistivity saturation" to a temperature-independent value of the order of the quantum of resistivity - the first analytically tractable model to do so. The saturation is not due to a fundamental limit on the electron lifetime, but rather to the appearance of a second conductivity channel. This is suggestive of the phenomenological "parallel resistor formula", known to describe the resistivity of a variety of saturating metals.