MICROSCOPIC THEORY OF ANDERSON LOCALIZATION IN A MAGNETIC-FIELD

A microscopic diagrammatic Green's function theory is developed for th e Anderson localization of a disordered two-dimensional electron gas u nder the influence of a weak external magnetic field. Using symmetry-a dapted representations for the correlation functions, the influence of the magnetic field on the pole structure of the vertex function is in vestigated. A self-consistent effective potential is constructed from a class of diagrams, which are relevant if the quantum corrections to the conductivity are not completely suppressed by the magnetic field. Simple ladder diagrams do not play any significant role. The microscop ic theory generalizes the self-consistent treatment derived by Vollhar dt and Wolfle [in Electronic Phase Transitions, edited by W. Hanke and Y. V. Kopaev (Elsevier, Amsterdam, 1992); Phys. Rev. B 22, 4666 (1980 )] to the case of weak nonzero magnetic fields and justifies our forme r phenomenological approach to the problem.