SUPPRESSION OF CHAOTIC DYNAMICS AND LOCALIZATION OF 2-DIMENSIONAL ELECTRONS BY A WEAK MAGNETIC-FIELD

We study a two-dimensional motion of a charged particle in a weak rand om potential and a perpendicular magnetic field. The correlation lengt h of the potential is assumed to be much larger than the de Broglie wa velength. Under such conditions, the motion on not too large length sc ales is described by classical equations of motion. We show that the p hase-space averaged diffusion coefficient is given by the Drude-Lorent z formula only at magnetic fields B smaller than certain value B-c. At larger fields, the chaotic motion is suppressed and the diffusion coe fficient becomes exponentially small. In addition, we calculate the qu antum-mechanical localization length as a function of B at the minima of sigma(xx). At B<B-c it is exponentially large but decreases with in creasing B. At B>B-c, this decrease becomes very rapid and the localiz ation length ceases to be exponentially large at a field B, which is only slightly larger than B-c. Implications for the crossover from the Shubnikov-de Haas oscillations to the quantum Hall effect are discuss ed.