Theory of universal incoherent metallic transport

Abstract

The anomalous transport of important materials such as high-temperature superconductors and other ‘bad metals’ is not well understood theoretically. In an incoherent metal, transport is controlled by the collective diffusion of energy and charge rather than by quasiparticle or momentum relaxation. Here, we explore the possibility of a universal bound D ≳ ℏνF2/(kBT) on the underlying diffusion constants in an incoherent metal. Such a bound is loosely motivated by results from holographic duality, the uncertainty principle and measurements of diffusion in strongly interacting non-metallic systems. Metals close to saturating this bound are shown to have a linear-in-temperature resistivity with an underlying dissipative timescale matching that recently deduced from experimental data on a wide range of metals. This bound may therefore be responsible for the ubiquitous appearance of high-temperature regimes in metals with T-linear resistivity. To establish this calls for direct measurements of diffusive processes and of charge susceptibilities in incoherent metals. Linear resistivity across many strongly correlated materials at high temperatures has no satisfactory explanation. A universal framework of incoherent metallic transport in which quantities are bounded could be the way forward.