Current fluctuations near to the 2D superconductor-insulator quantum critical point

Systems near to quantum critical points show universal scaling in their response functions. We consider whether this scaling is reflected in their fluctuations; namely in current-noise. Naive scaling predicts low-temperature Johnson noise crossing over to noise power $\propto E^{z/(z+1)}$ at strong electric fields. We study this crossover in the metallic state at the 2d z=1 superconductor/insulator quantum critical point. Using a Boltzmann-Langevin approach within a 1/N-expansion, we show that the current noise obeys a scaling form $S_j=T \Phi[T/T_{eff}(E)]$ with $T_{eff} \propto \sqrt{E}$. We recover Johnson noise in thermal equilibrium and $S_j \propto \sqrt{E}$ at strong electric fields. The suppression from free carrier shot noise is due to strong correlations at the critical point. We discuss its interpretation in terms of a diverging carrier charge $\propto 1/\sqrt{E}$ or as out-of-equilibrium Johnson noise with effective temperature $\propto \sqrt{E}$.