The inter-edge-channel equilibration length ${\mathit{L}}_{\mathrm{eq}}$ of a high-mobility two-dimensional electron gas in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructure is studied in the range of magnetic fields 2.8–4.5 T at temperatures of 0.5≤T≤11 K. The inverse of ${\mathit{L}}_{\mathrm{eq}}$ increases with increasing T at a magnetic field (3.4 T) corresponding to the center of the ν=4 Hall plateau, and rapidly decreases with increasing magnetic field B to depart from the center of the plateau. An analysis of these data in terms of impurity and phonon scatterings is attempted by assuming a parabolic-type confining potential. The observed T and B dependences are consistently analyzed if the inter-edge-state spacing ΔX is assumed to be (i) much larger than the magnetic length ${\mathit{l}}_{\mathit{B}}$ (ΔX=530 Å, ${\mathit{l}}_{\mathit{B}}$∼130 Å) and (ii) kept nearly unchanged in the range of magnetic fields studied. That the size of ΔX is nearly independent of B is an unexpected behavior, which disagrees also with recent self-consistent calculations of the edge-confining potential. The validity of the assumed parabolic-type confining potential is discussed.

• Received 6 July 1995

DOI:https://doi.org/10.1103/PhysRevB.52.11159