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

The electrical resistivity of conventional metals varies linearly with temperature T in the regime T > ω₀, where ω₀ is a characteristic phonon frequency. The corresponding transport scattering rate is 1/τ_tr = 2π λT, 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 quasi-elastic in this regime, it is unlikely that Planckian considerations are relevant. We present 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 may apply to metals more generally.