A stability bound on the $T$-linear resistivity of conventional metals

TL;DR

This paper investigates the limits of electron-phonon coupling in conventional metals, demonstrating a stability bound on the coupling strength that ensures metallic transport, challenging the relevance of Planckian bounds in this context.

Contribution

The study introduces a stability bound on the electron-phonon coupling strength in metals, supported by Monte Carlo simulations of the Holstein model, providing a new perspective on transport limits.

Findings

Monte Carlo results show a stability bound on coupling strength.

The bound is consistent with metallic transport.

Planckian bounds are not relevant in this regime.

Abstract

Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is $1/\tau_\text{tr} = 2\pi \lambda T$, where $\lambda$ is a dimensionless strength of the electron-phonon coupling. The fact that measured values satisfy $\lambda \lesssim 1$ has been noted in the context of a possible "Planckian" bound on transport. However, since the electron-phonon scattering is quasi-elastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a "stability" bound on $\lambda$ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.