Non linear transport theory for negative-differential resistance states of two dimensional electron systems in strong magnetic fields

We present a model to describe the nonlinear response to a direct dc current applied to a two-dimensional electron system in a strong magnetic field. The model is based on the solution of the von Neumann equation incorporating the exact dynamics of two-dimensional damped electrons in the presence of arbitrarily strong magnetic and dc electric fields, while the effects of randomly distributed impurities are perturbatively added. From the analysis of the differential resistivity and the longitudinal voltage we observe the formation of negative differential resistivity states (NDRS) that are the precursors of the zero differential resistivity states (ZDRS). The theoretical predictions correctly reproduce the main experimental features provided that the inelastic scattering rate obey a $T^2$ temperature dependence, consistent with electron-electron interaction effects.