Non-Markovian effects on the two-dimensional magnetotransport: Low-field anomaly in magnetoresistance

We discuss classical magnetotransport in a two-dimensional system with strong scatterers. Even in the limit of very low field, when omega(c)tau<1 (omega(c) is the cyclotron frequency, tau is the scattering time) such a system demonstrates strong negative magnetoresistance caused by non-Markovian memory effects. A regular method for the calculation of non-Markovian corrections to the Drude conductivity is presented. A quantitative theory of the recently discovered anomalous low-field magnetoresistance is developed for the system of two-dimensional electrons scattered by hard disks of radius a, randomly distributed with concentration n. For small magnetic fields the magentoresistance is found to be parabolic and inversely proportional to the gas parameter, deltarho(xx)/rhosimilar to-(omega(c)tau)(2)/na(2). In some interval of magnetic fields the magnetoresistance is shown to be linear deltarho(xx)/rhosimilar to-omega(c)tau in a good agreement with the experiment and numerical simulations. Magnetoresistance saturates for omega(c)tau>na(2), when the anomalous memory effects are totally destroyed by the magnetic field. We also discuss magnetotransport at very low fields and show that at such fields magnetoresistance is determined by the trajectories having a long Lyapunov region.