Crossover from the nonuniversal scaling regime to the universal scaling regime in quantum Hall plateau transitions

Abstract

We present in this Brief Report our experimental results on the quantum Hall plateau-to-plateau transition in long-range Coulombic disordered two-dimensional electron systems embedded in the ${\text{Al}}_{x}{\text{Ga}}_{1\ensuremath{-}x}{\text{As-Al}}_{0.32}{\text{Ga}}_{0.68}\text{As}$ heterostructures (with $x=0\mathrm{%}$ and 0.21%) in a large temperature range from 1.2 K down to 1 mK. In these samples a crossover behavior is observed from the high-temperature, nonuniversal scaling regime to the low-temperature, universal scaling regime, with the temperature exponent $\ensuremath{\kappa}$ changing from $\ensuremath{\kappa}=0.58$ to 0.42, respectively. The crossover temperature increases with increasing $x$, from 120 mK for $x=0\mathrm{%}$ to 250 mK for $x=0.21\mathrm{%}$. When the Al concentration reaches $x=0.85\mathrm{%}$ at which the short-range random alloy potential dominates the disorder, the crossover temperature is beyond 1.2 K and the universal scaling is observed over two decades of temperature.