Theory of Anderson localization in an electric field

A microscopic diagrammatic theory of Anderson localization under the influence of a constant electric field has been worked out on the basis of the Keldysh formalism, where the main localizing processes are comprised into a self-consistent effective potential. A direct influence of the electric field on the pole structure of the diffusion function is detected. This leads to the appearance of a delocalization edge. In the vicinity of the metal-insulator phase transition the Einstein relation is extended to a relationship between the spectral drift mobility and the spectral diffusion coefficient, which gives rise to a nonlinear field dependence. For isotropic electronic systems and energy-independent renormalized scattering times the presented theory justifies our former phenomenological approach concerning the electric-field effects on Anderson localization.