LOCALIZED ELECTRONS IN A MAGNETIC FIELD

Abstract

We briefly review recent developments on the response of localized electrons to an external magnetic field. They originate from subtle interference effects between forward-scattered paths which, in the localized regime, make the dominant contribution to the transition amplitude. On a lattice the correlations between the paths produce self-similar (quasiperiodic) spatial interference patterns for commensurate (incommensurate) ratios of the applied magnetic flux per plaquette with the flux quantum. If localization is due to strong disorder (as in lightly doped semiconductors), this is augmented by a logarithmic averaging. They give rise to striking quantum interference phenomena observed in mesoscopic and macroscopic insulators: Aharonov-Bohm oscillations with periods of one and one half flux-quantum, the Hall effect, pronounced conductance fluctuations, and anomalous negative (and positive in presence of spin-orbit scattering) magnetoresistance. The theoretical works based on the “directed paths” approach are reviewed. Experimental results which motivated these works, are summarized.