Effect of long-range potential fluctuations on scaling in the integer quantum Hall effect

We report a set of transport data taken in two low-mobility GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructures. When T>200 mK, we find that the T dependence of (d${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$/dB${)}^{\max }$ behaves differently in different Landau levels, whereas when T<200 mK, it behaves like ${\mathit{T}}^{\mathrm{-}0.42}$ as reported by Wei et al. [Phys. Rev. Lett. 61, 1294 (1988)]. The characteristic T (=200 mK) for observing the critical behavior is much lower than that of previous observations in the ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/InP heterostructure. This lowering of T for scaling is attributed to the dominance of long-range potential fluctuations due to the remote ionized impurities in the ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As.