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 > ω_0, where ω_0 is a characteristic phonon frequency. The corresponding transport scattering rate of electrons is 1/τ_tr = 2π λT, where λ is a dimensionless strength of the electron-phonon coupling. The fact that experimentally measured values satisfy λ <~ 1 is striking---especially because in the conventional theory of metals, λ is not a-priori bounded---and has been noted in the context of a conjectured "Planckian" bound on transport. The appeal of such a universal bound is that, if correct, it might also govern the strange metallic behavior observed in a variety of correlated electron materials, which exhibit T-linear resistivity extending down to low temperatures T << ω_0, the microscopic origin of which remains a matter of heated debate.

However, Planckian considerations in general apply only to the "inelastic" scattering rate, whereas electron-phonon scattering is quasi-elastic at T > ω_0. Hence, even if the Planckian bound were true, it would not explain the observed bound on λ in conventional metals at high temperatures. I will discuss recent Monte Carlo results on the paradigmatic Holstein model which show that a very different sort of bound is at play here: a "stability" bound on λ consistent with metallic transport [4]. I will then speculate that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.