Selective equilibration among the current-carrying states in the quantum Hall regime

The Hall resistance of a two-dimensional electron gas is measured with gated probes to determine the extent of equilibration among the N current-carrying states in the quantum Hall regime. After traveling macroscopic distances ({~}80 {μ}m), current injected into the first state is equilibrated among the N-1 lowest states but equilibration into the highest state varies strongly across the Hall plateau. This is attributed to a change in the Nth state from being localized within a magnetic length of the edge to substantially extending into the sample.