  It is well known that electrically neutral excitons can still be affected by
crossed electric and magnetic fields that make them move in a direction
perpendicular to both fields. We show that a similar effect appears in the
absence of external electric fields, in the case of scattering of an exciton
flow by charged impurities in the presence of the external magnetic field. As a
result, the exciton flow changes the direction of its propagation that may be
described in terms of the Hall conductivity for excitons. We develop a theory
of this effect, which we refer to as the anomalous exciton Hall effect, to
distinguish it from the exciton Hall effect that arises due to the valley
selective exciton transport in transition metal dichalcogenides. According to
our estimations, the effect is relatively weak for optically active or bright
excitons in conventional GaAs quantum wells, but it becomes significant for
optically inactive or dark excitons, because of the difference of the
lifetimes. This makes the proposed effect a convenient tool for spatial
separation of dark and bright excitons.
