A new approach to non-linear transport for an electron-impurity system in a static electric field

A new approximate approach to steady-state non-linear electronic transport in a static electric field is developed for the system composed of interacting electrons with randomly distributed impurities. Starting from the separation of the centre-of-mass variables from the relative variables of the electrons the authors obtain a density matrix describing the relative motion of electrons to the first order of the impurity potential, but arbitrarily strong electric field. From this density matrix the force-balance equation for the steady state is derived, which can be expressed by a density-density correlation function and thus can easily be calculated diagrammatically. The formulae obtained are applied to the calculation of the non-linear impurity resistivity in the degenerate case and in the Maxwell-Boltzmann case, showing the simplicity and effectiveness of the method.