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/ τ tr  = 2 π λ T , where λ is a dimensionless strength of the electron–phonon coupling. The fact that measured values satisfy λ  ≲ 1 has been noted in the context of a possible “Planckian” bound on transport. However, since the electron–phonon scattering is quasielastic 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 λ 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.