Nonlinear conductivity of a holographic superconductor under constant electric field

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 times, 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 ∼E-2/3 when the system is close to the critical temperature Tc, which agrees with predictions from solving the time-dependent Ginzburg-Landau equation. Away from Tc, the E-2/3 scaling of the conductivity still holds when E is large.