Theory of universal incoherent metallic transport

Abstract: In an incoherent metal, transport is controlled by the collective diffusion of energy and charge rather than by quasiparticle or momentum relaxation. We explore the possibility of a universal bound $D \gtrsim \hbar v_F^2/(k_B T)$ on the underlying diffusion constants in an incoherent metal. Such a bound is loosely motivated by results from holographic duality, the uncertainty principle and from 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. The phenomenology of universal incoherent transport is found to reproduce various further observations in strongly correlated metals, and motivates direct probes of diffusive processes and measurements of charge susceptibilities. We suggest that this bound may be responsible for the ubiquitous appearance of high temperature regimes in metals with $T$-linear resistivity.