Disorder and the integer quantum Hall plateau-to-plateau transition

We have studied the temperature scaling of integer quantum Hall plateau-to-plateau transition in various disordered systems down to 10mK. The samples are Al$_{x}$Ga$_{1-x}$As-Al$_{0.33}$Ga$_{0.67}$As heterostructures with different Al concentration $x$. Previous work has shown a perfect power law (dR$_{xy}$/dB)$\vert _{Bc}\propto $T$^{-\kappa }$ with $\kappa $=0.42 over two decades of temperatures in the sample with $x$=0.85{\%}. In the sample of $x$=0, $\kappa $=0.58 was observed at high temperatures, while we have now found $\kappa $=0.42 restored below a crossover temperature T$_{c}$=120mK. T$_{c}$ increases to 250mK for $x$=0.21{\%}, and is not observable in the experimental temperature range in the sample of $x$=0.85{\%}. We propose that the quantum phase coherence length exceeds the disorder correlation length below T$_{c}$, shifting the nature of the disorder in the system from long-ranged to short-ranged. On the other end of the sample series with $x$=4.1{\%}, where alloy clustering is believed to be significant, $\kappa $=0.58 is found to persist down to the lowest temperature of the measurement limit, suggesting a different universal class of the transition in long-range disordered systems.