Nonlinear transport near a quantum phase transition in two dimensions

The nonlinear transport near a quantum phase transition for the dissipative insulator-superconductor phase transition was studied within Landau theory. The scaling function for the nonlinear conductivity in the quantum disordered regime was obtained using the Green function formalism. It was found that the conductivity scaled as E² at low fields but crossed over the large fields to a universal constant. The crossover between these two regimes was obtained when the length scale for the quantum fluctuations became comparable to that of the electric field within logarithmic accuracy.