Magnetic-field dependence of the quantum-Hall-liquid–insulator transition

We present measurements of the magnetic field dependence of the insulator transition in a gated ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs heterostructure. The resulting phase diagram shows reentrant behavior as the magnetic length decreases below the zero-field electron mean free path. By fitting our data to a predicted phase diagram, we obtain a value for the localization length exponent governing the quantum-Hall-liquid–insulator transition. As has been recently suggested, this value is in agreement with that determined for the critical exponent between quantum Hall plateaus.