Dynamical stability and filamentary instability in holographic conductors

TL;DR

This paper investigates the dynamical stability of holographic conductors modeled by the D3-D7 system, revealing conditions under which states become unstable and lead to filamentary inhomogeneities due to nonlinear conductivity effects.

Contribution

It provides a detailed analysis of stability and instability regions in holographic conductors, identifying the emergence of inhomogeneous steady states with current filaments.

Findings

Low-current states can be dynamically unstable.

Stability switching occurs at the $J$-$E$ turning point.

Inhomogeneous steady states with current filaments exist.

Abstract

In this study, we analyze the dynamical stability of the D3-D7 model dual to a holographic conductor with a constant current under an external electric field. We particularly focus on the stability around the parameter region where the multivalued relation between the external electric field and the current is shown due to nonlinear conductivity. The dynamical stability of the states can be analyzed by considering linear perturbations in the background states and computing the quasinormal modes. In the multivalued region, we find that the states in one branch with a low electric current can be dynamically unstable. The turning point in the $J$-$E$ characteristic coincides with the stability switching. Further, we also find that the perturbations around the unstable states can become stable with finite wavenumber. In other words, the perturbations in the background states become static at a critical wavenumber, implying the existence of inhomogeneous steady states with current filaments.