The edge structure of a gate-defined compressible quantum Hall fluid in the filling fraction range $\frac{2}{3}$ to 1 is studied using the three reconstructed $e^2/3h$ fractional edge modes of a unity filling integer quantum Hall state. We find that the individually excited partially resolved $e^2/3h$ edge modes of the bulk state equilibrate completely even at higher magnetic field when passing through the gate-defined compressible fluid with filling between $\frac{2}{3}$ and 1. This result is unexpected because edge reconstruction at the smooth boundary is generally expected due to dominant incompressibility at filling $\frac{2}{3}$ and $\frac{1}{3}$. Recently, such a reconstructed edge mode has been reported for the compressible fluid in the filling fraction range $\frac{1}{3}$ to $\frac{2}{3}$. In contrast, equilibration of fractional edge modes in the compressible fluid within the filling fraction range $\frac{2}{3}$ to 1 becomes faster with increasing magnetic field. This anomalous result will stimulate further investigations on edge structure in these complex many-body systems.

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• Edge states
• Fractional quantum Hall effect
• Integer quantum Hall effect
• III-V semiconductors
• Two-dimensional electron system
• Dilution refrigerator