We investigate high-mobility two-dimensional electron gases in AlGaAs
heterostructures by employing Schottky-gate-dependent measurements of the
samples' electron density and mobility. Surprisingly, we find that two
different sample configurations can be set in situ with mobilities diering by a
factor of more than two in a wide range of densities. This observation is
discussed in view of charge redistributions between the doping layers and is
relevant for the design of future gateable high-mobility electron gases
