Inter-edge-state scattering and nonlinear effects in a two-dimensional electron gas at high magnetic fields

Charge-carrier transport in the presence of a nonequilibrium population of edge states is studied both theoretically and experimentally. The attention is focused on the temperature dependence of the inter-edge-state (IES) electron scattering and on nonlinear effects of the edge-state transport, both in the integer-quantum-Hall-effect regime. First, a theoretical analysis of the IES transition is developed, which explicitly considers the Fermi distribution function of electrons in edge states and takes account of both a long-range impurity scattering and the acoustical-phonon scattering. The analysis explains well the observed temperature dependence of the IES equilibration length in high-mobility GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructure devices when a smooth parabolic edge potential is assumed. Second, analysis of nonlinear transport across a potential barrier predicts an inverted population of electrons in edge states, which explains asymmetric energy dissipation around the barrier recently observed by other authors. Furthermore, the analysis predicts a nonlinear two-terminal resistance of the potential barrier, which provides a reasonable account for the experimentally observed resistance. Third, nonlinear effects are reported in which the edge states reorganize themselves in the presence of a nonequilibrium population of electrons. This leads to a population-dependent IES equilibration length, which accounts for an observed nonlinear Hall resistance which is asymmetric about I=0. The onset of the IES spontaneous acoustic-phonon emission is observed when the amplitude of the unequal population between relevant edge states exceeds a threshold. Finally, experimental evidence is presented to show that the maximum amplitude to which adjacent edge states can be unequally populated is limited to one-half the value of the Landau-level-energy spacing ħ${\mathrm{\omega }}_{\mathit{c}}$.