The possibility of Anderson localization of electrons in a disordered solid in d dimensions in the presence of a finite, uniform electric field is discussed. The self-consistent diagrammatic theory of localization developed for zero fields is generalized to treat the case of a finite electric field. In one-dimensional systems this theory is shown to reproduce the exact results of Prigodin except for some minor differences. For weak fields, or strong disorder, there is power-law localization and for stronger fields there is a mobility edge past which the states are extended. In higher dimensions the self-consistent theory leads to the conclusion that Anderson localization is not possible in finite electric fields. Simple arguments indicate that this conclusion is independent of the self-consistent theory.

• Received 14 June 1985

DOI:https://doi.org/10.1103/PhysRevB.33.780