Theory of universal incoherent metallic transport

TL;DR

This paper investigates a potential universal lower bound on diffusion constants in incoherent metals, linking it to linear resistivity and experimental observations, and discusses its implications for understanding high-temperature metallic behavior.

Contribution

It proposes a universal bound on diffusion constants in incoherent metals, connecting holographic duality, the uncertainty principle, and experimental data to explain T-linear resistivity.

Findings

Metals near the bound exhibit T-linear resistivity.

The bound correlates with dissipative timescales from experiments.

High-temperature regimes in metals may be explained by this diffusion bound.

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. This bound may be responsible for the ubiquitous appearance of high temperature regimes in metals with $T$-linear resistivity, motivating direct probes of diffusive processes and measurements of charge susceptibilities.