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 $h\mathrm{/}{e}^2$ 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 $h\mathrm{/}{e}^2$ for all values of the scaling parameter $\mathrm{\Delta }\nu \mathrm{/}(T\mathrm{/}{T}_0{)}^{\kappa }$ with $\mathrm{\Delta }\nu =\nu -{\nu }_c$. However, as a function of $\mathrm{\Delta }\nu$ (or magnetic field) the Hall resistance diverges in the limit $T\to 0$ for all values $\nu <{\nu }_c$.