Nonlinear Conductivity of a Holographic Superconductor Under Constant Electric Field

TL;DR

This paper investigates the nonlinear electrical response of a holographic superconductor under a constant electric field, revealing how the current and conductivity behave near the critical temperature using gauge/gravity duality.

Contribution

It provides a novel analysis of the nonlinear conductivity and pair breaking current in holographic superconductors under constant electric fields, aligning with Ginzburg-Landau predictions.

Findings

Peak current increases linearly with electric field.

Superconducting gap vanishes at late times, indicating a transition to normal phase.

Nonlinear conductivity scales as E^{-2/3} near critical temperature.

Abstract

The dynamics of a two-dimensional superconductor under a constant electric field $E$ is studied by using the gauge/gravity correspondence. The pair breaking current induced by $E$ first increases to a peak value and then decreases to a constant value at late time, where the superconducting gap goes to zero, corresponding to a normal conducting phase. The peak value of the current is found to increase linearly with respect to the electric field. Moreover, the nonlinear conductivity, defined as an average of the conductivity in the superconducting phase, scales as $\sim E^{-2/3}$ for large $E$ when the system is close to the critical temperature, which agrees with predictions from solving the time dependent Ginzburg-Landau equation.