Beyond Drude transport in hydrodynamic metals

TL;DR

This paper investigates the effects of momentum-relaxing gradient corrections beyond the Drude model in hydrodynamic metals, revealing their impact on conductivities and explaining experimental observations in strongly-coupled and near-Fermi-liquid metals.

Contribution

It introduces the structure and physical implications of subleading gradient corrections in hydrodynamic theories of metals, extending the understanding beyond the traditional Drude model.

Findings

Gradient corrections renormalize the Drude pole weight in conductivities.

Additional derivative corrections modify cyclotron frequency and Hall conductivity.

Effective mass measurements differ in strongly-coupled metals near Fermi liquids.

Abstract

In interacting theories, hydrodynamics describes the universal behavior of states close to local thermal equilibrium at late times and long distances in a gradient expansion. In the hydrodynamic regime of metals, momentum relaxes slowly with a rate $\Gamma$, which formally appears on the right-hand side of the momentum dynamical equation and causes a Drude-like peak in the frequency dependence of the thermoelectric conductivities. Here we study the structure and determine the physical implications of momentum-relaxing gradient corrections beyond Drude, \emph{i.e.} arising at subleading order in the gradient expansion. We find that they effectively renormalize the weight of the Drude pole in the thermoelectric conductivities, and contribute to the dc conductivities at the same order as previously-known gradient corrections of translation-invariant hydrodynamics. Turning on a magnetic field, extra derivative corrections appear and renormalize the cyclotron frequency and the Hall conductivity. This relaxed hydrodynamics provides a field-theoretic explanation for previous results obtained using gauge-gravity duality. In strongly-coupled metals where quasiparticles are short-lived and which may be close to a hydrodynamic regime, the extra contributions we discuss are essential to interpret experimentally measured magneto-thermoelectric conductivities. Specializing to metals close to a Fermi liquid phase, the effective mass measured either through the specific heat or the spectral weight of the Drude-like peak are found to differ, as was indeed reported in overdoped cuprate superconductors. More generally, we expect such terms to be present in any hydrodynamic theory with approximate symmetries, which arise in many physical systems.