  Scanning gate microscopy is used to locally investigate electron transport in
a high-mobility two-dimensional electron gas formed in a GaAs/AlGaAs
heterostructure. Using quantum point contacts (QPC) we observe branches caused
by electron backscattering decorated with interference fringes similar to
previous observations by Topinka et al. We investigate the branches at
different points of a conductance plateau as well as between plateaus, and
demonstrate that the most dramatic changes in branch pattern occur at the
low-energy side of the conductance plateaus. The branches disappear at magnetic
fields as low as 50 mT demonstrating the importance of backscattering for the
observation of the branching effect. The spacing between the interference
fringes varies by more than 50% for different branches across scales of
microns. Several scenarios are discussed to explain this observation.
