Nonlinear response in overlapping and separated Landau levels of GaAs quantum wells

We have studied magnetotransport properties of a high-mobility two-dimensional electron system subject to weak electric fields. At low magnetic field $B$, the differential resistivity acquires a correction $\delta r \propto -\lambda^2 j^2/B^2$, where $\lambda$ is the Dingle factor and $j$ is the current density, in agreement with theoretical predictions. At higher magnetic fields, however, $\delta r$ becomes $B$-independent, $\delta r \propto -j^2$. While the observed change in behavior can be attributed to a crossover from overlapping to separated Landau levels, full understanding of this behavior remains a subject of future theories.