Nonlinear Transport in a Two Dimensional Holographic Superconductor

TL;DR

This paper investigates nonlinear electrical transport in a two-dimensional holographic superconductor, revealing how conductivity varies from linear to nonlinear and chaotic regimes under different electric field strengths.

Contribution

It introduces a holographic approach to analyze nonlinear and far-from-equilibrium transport phenomena in 2D superconductors, including chaotic behavior of the superconducting gap.

Findings

Weak electric field yields linear conductivity with a gap.

Strong electric field induces a quadratic nonlinear conductivity.

At high fields, the system reaches a universal linear conductivity of one.

Abstract

The problem of nonlinear transport in a two dimensional superconductor with an applied oscillating electric field is solved by the holographic method. The complex conductivity can be computed from the dynamics of the current for both near- and non-equilibrium regimes. The limit of weak electric field corresponds to the near equilibrium superconducting regime, where the charge response is linear and the conductivity develops a gap determined by the condensate. A larger electric field drives the system into a superconducting non-equilibrium steady state, where the nonlinear conductivity is quadratic with respect to the electric field. Keeping increasing the amplitude of applied electric field results in a far-from-equilibrium non-superconducting steady state with a universal linear conductivity of one. In lower temperature regime we also find chaotic behavior of superconducting gap, which results in a non-monotonic field dependent nonlinear conductivity.