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Theory of universal incoherent metallic transport

Sean A. Hartnoll

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.

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 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 -linear resistivity, motivating direct probes of diffusive processes and measurements of charge susceptibilities.

Paper Structure

This paper contains 9 sections, 30 equations, 2 figures.

Table of Contents

  1. Introduction
  2. From quasiparticle to incoherent transport
  3. Bounds on transport coefficients
  4. Experimental consequences
  5. Final comments
  6. Methods
  7. Acknowledgements

Figures (2)

  • Figure 1: Quasiparticle bounds versus incoherent bounds: Schematic illustration of the role of the Mott-Ioffe-Regel bound and the proposed diffusivity bound in the resistivity versus temperature plane.
  • Figure 2: Lorenz ratio as a function of temperature. Estimated using a Fermi-Dirac distribution for two dimensional electrons to compute the thermodynamic susceptibilities in (\ref{['eq:L']}). Temperature $T$, chemical potential $\mu$ and bandwidth cutoff on the single particle energy taken (for illustrative purposes) to be $E_B = 2 \mu$.