Nonlinear Transport Near a Quantum Phase Transition in Two Dimensions

TL;DR

This paper develops a theoretical framework to understand nonlinear electrical transport near a quantum phase transition in two-dimensional systems, revealing a crossover from quadratic to constant conductivity with increasing electric field.

Contribution

It introduces a non-equilibrium Green function approach to derive the scaling function for nonlinear conductivity in the dissipative insulator-superconductor transition.

Findings

Conductivity scales as E^2 at low fields

At high fields, conductivity approaches a universal constant of order e^2/h

Crossover determined by quantum fluctuation length scale and electric field

Abstract

The problem of non-linear transport near a quantum phase transition is solved within the Landau theory for the dissipative insulator-superconductor phase transition in two dimensions. Using the non-equilibrium Schwinger round-trip Green function formalism, we obtain the scaling function for the non-linear conductivity in the quantum disordered regime. We find that the conductivity scales as $E^2$ at low field but crosses over at large fields to a universal constant on the order of $e^2/h$. The crossover between these two regimes obtains when the length scale for the quantum fluctuations becomes comparable to that of the electric field within logarithmic accuracy.