  The pattern of branched electron flow revealed by scanning gate microscopy
shows the distribution of ballistic electron trajectories. The details of the
pattern are determined by the correlated potential of remote dopants with an
amplitude far below the Fermi energy. We find that the pattern persists even if
the electron density is significantly reduced such that the change in Fermi
energy exceeds the background potential amplitude. The branch pattern is robust
against changes in charge carrier density, but not against changes in the
background potential caused by additional illumination of the sample.
