Experiments on scaling in AlxGa1−xAs/GaAs heterostructures under quantum Hall conditions

Abstract

The influence of repulsive (Be) and attractive (Si) scattering centers on the temperature-dependent half-width of the Shubnikov–de Haas peaks ΔB(T) and the maximum of the slope of the Hall resistance ∂${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$/∂B has been investigated at millikelvin temperatures for the two-dimensional electron gas in ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs heterostructures. Both sheet-doped and homogeneously doped samples were studied. In contrast to results reported for ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/InP heterostructures, where a scaling exponent κ=0.42±0.04 with ΔB∝${\mathit{T}}^{\mathrm{\kappa }}$ and (∂${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$/∂B${)}^{\max }$∝${\mathit{T}}^{\mathrm{-}\mathrm{\kappa }}$ is found and suggested to be universal, our data lead to scaling exponents that systematically increase with decreasing mobility. The transition between the integer filling factor 1 and the fractional filling factor 2/3 has been studied and a scaling behavior observed.