Alloy-disorder scattering of the interacting electron gas in quantum wells and heterostructures of Al$_x$Ga$_{1-x}$As

The question whether alloy disorder is screened or unscreened is of fundamental importance. Therefore, we calculate the mobility of the interacting two-dimensional electron gas as realized in Al$_x$Ga$_{1-x}$As quantum wells and heterostructures in the presence of alloy-disorder scattering. For the screening we use the random-phase approximation and we include many-body effects due to exchange and correlation. We propose to determine the alloy disorder potential $V_{\text{AD}}$ from mobility measurements. If we use $V_{\text{AD}}=1.04\,$eV we can explain recent experimental results obtained for quantum wells and heterostructures with ultrahigh mobility. From the anomalous linear temperature dependence of the mobility measured in heterostructures we conclude that the alloy disorder is screened. More experiments are needed to confirm the screening of the alloy disorder and we propose some measurements.