Quenching of scattering in mesoscopic systems in the quantum Hall regime.

Abstract

We study theoretically the elastic and inelastic scattering of the edge states of quasi-one-dimensional and quasi-two-dimensional electron systems in the presence of magnetic fields. We obtain a large mean free path (l\ifmmode\bar\else\textasciimacron\fi{}) as it has been experimentally observed. The Born approximation in the case of impurities and a deformation-potential scheme in the case of acoustic phonons is used to calculate the lifetime and mean free path of a carrier in one of the edge states. The magnitude that characterizes the efficiency of the scattering is the center of gravity of the edge-state wave function, which differs from the semiclassical center of the orbit in the ratio of the velocity of the state to the cyclotron frequency. When both inter- and intra-edge-state mechanisms for scattering coexist, the latter dominates for high fields, giving a monotonically decreasing mean free path as B increases. However, when the filling conditions just allow the inter-edge-state mechanism, l\ifmmode\bar\else\textasciimacron\fi{} has a minimum as a function of B. In this case, the elastic impurity contribution dominates and the scattering is suppressed by the magnetic field faster than exponentially. Such a quenching is much more efficient when the energy of the initial edge state is close to that of a bulk Landau level, in agreement with the available experimental information.