Abstract
Non-Ohmic and sample-size-dependent transport effects [i.e., Shubnikov--de Haas (SdH) and quantum Hall effect] of mesoscopic two-dimensional (2D) systems prove the occurrence of nonlocal contributions to the electronic conductance in these systems. However, this nonlocal regime accompanied by a non- equilibrium population of the edge states with respect to the 2D bulk state is quenched at rather low values of external electric fields or flowing currents, respectively. Beyond this quench, the bulk state is coupled to the edge by an increasing amount of electron transitions between the corresponding states. We analyze the non-Ohmic behavior of SdH oscillations at GaAs/${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum Hall conductors on the basis of a model including edge and bulk transport. We deduce the current-dependent non- equilibrium population of edge and bulk states quantitatively. Further, we give estimates for the current ranges in which transitions of electrons between edge and bulk states due to elastic and inelastic scattering are relevant. The change of the typical nonequilibrium parameters as the equilibration length and the maximal difference of chemical potentials of edge and bulk states in tilted magnetic fields are also discussed.
Published Version
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