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The Hall resistance of a two-dimensional electron gas is measured with gated probes to determine the extent of equilibration among the TV current-carrying states in the quantum Hall regime. After traveling macroscopic distances (-80 /im), current injected into the first state is equilibrated among the TV-1 lowest states but equilibration into the highest state varies strongly across the Hall plateau. This is attributed to a change in the TVth state from being localized within a magnetic length of the edge to substantially extending into the sample. channels. 3 As this current travels along an edge it "equilibrates" by which we mean it tends to redistribute so that an equal fraction of the current is carried by each edge channel. Current equilibration takes place via electron-scattering processes, the required potential being provided by disorder or phonons. By using one nonideal probe as a current injector, and a second nonideal probe as a current detector, the extent of equilibration that occurs between the nonideal probes can be determined. If the spatial separation between the edge channels is not much greater than the magnetic length, equilibration is expected to occur after current travels a distance on the order of the zero-field inelastic and elastic lengths (-10 /im). Recently, van Wees et al. have shown that for high magnetic fields and over a distance of -1 /im no equilibration occurs. 3 Other experiments 4,5 have been interpreted as implying the surprising result that no equilibration occurs for distances of 100 //mor more.Contrary to this interpretation, our experiments indicate that with TV available edge channels the current is always equilibrated among the TV-1 lowest 6 channels after traveling distances -80 /zm. We find further that the fraction of current that redistributes into the TVth channel decreases dramatically as the center of the corresponding Landau level approaches E F . It is the decoupling of this channel, rather than a general effect among all edge channels, that has been observed in previous experiments. 4 ' 5 We believe that this provides a new understanding of the current-carrying states. Current equilibrates among the TV -1 channels existing near the edge of the sample. However, the TVth channel spreads into the sample as the TVth Landau level approaches £>, causing a decrease in scattering between it and the true edge channels.Our device [ Fig. 2(a)] is formed by etching an AlGaAs/GaAs heterostructure (electron density 3.4 xlO 11 cm -2 and mobility 500000 cm 2 /Vsec at 4.2 K) into a Hall bar. Nonideal probes are made by metallic gates with narrow openings of lithographic width 500 nm and length 300 nm on the probe leads. A negative volt-PACS numbers: 72.20.My, 73.40.Cg, 73.40.LqThe recently developed Biittiker formalism 1 has proved useful in understanding two-dimensional electronic systems in the quantum Hall regime. It is based on previous theories 2 in which the conducting properties are determined by states at the Fermi level, £>, located spatially near the edge of the samp...

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