Nonlinear conductivity and the ringdown of currents in metallic holography

TL;DR

This paper investigates the nonlinear electrical and heat transport dynamics in a holographic model with momentum relaxation, revealing oscillatory ringdown signatures and the conditions under which linear response approximations remain valid.

Contribution

It introduces a detailed analysis of nonlinear conductivity and current relaxation in holography, highlighting the impact of inhomogeneity and temperature effects on transport properties.

Findings

Currents return to equilibrium via quasi-normal modes with spectrum depending on inhomogeneity.

Signatures of incoherent transport manifest as oscillatory heat current ringdown.

Nonlinear conductivity at small electric fields aligns with linear response at an effective temperature.

Abstract

We study the electric and heat current response resulting from an electric field quench in a holographic model of momentum relaxation at nonzero charge density. After turning the electric field off, currents return to equilibrium as governed by the vector quasi-normal modes of the dual black brane, whose spectrum depends qualitatively on a parameter controlling the strength of inhomogeneity. We explore the dynamical phase diagram as a function of this parameter, showing that signatures of incoherent transport become identifiable as an oscillatory ringdown of the heat current. We also study nonlinear conductivity by holding the electric field constant. For small electric fields a balance is reached between the driving electric field and the momentum sink -- a steady state described by DC linear response. For large electric fields Joule heating becomes important and the black branes exhibit significant time dependence. In a regime where the rate of temperature increase is small, the nonlinear electrical conductivity is well approximated by the DC linear response calculation at an appropriate effective temperature.