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

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.

arXiv comment6 pages, 3 figures (+Appendices: 6 pages, 5 figures). Final version published in Proceedings of the National Academy of Sciences

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