Observation of the quantized Hall insulator in the quantum critical regime of the two-dimensional electron gas

We have investigated the Hall resistance \(R_H\) near the plateau-insulator transition of a two-dimensional electron gas in the quantum critical regime. High-field magnetotransport data taken on a low-mobility InGaAs/InP heterostructure with the plateau-insulator transition at a critical field \(B_c\) of 17.2 T show that the Hall resistance \(R_H\) is quantized at \(h/e^2\) near the critical filling fraction (\(\nu_c\) = 0.55) when \(T \to 0\). By making use of universal scaling functions extracted from the magnetotransport data we show that \(R_H\) in the insulating phase in the limit \(T \to 0\) is quantized at \(h/e^2\) for all values of the scaling parameter \(\Delta\nu /(T/T_0)^\kappa\) with \(\Delta\nu = \nu - \nu_c\). However, as a function of \(\Delta\nu \) (or magnetic field) the Hall resistance diverges in the limit \(T \to 0\) for all values \(\nu < \nu_c\).