Stable branched electron flow

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.