  The effect of an external in-plane electric field on neutral and charged
exciton states in two-dimensional (2D) materials is theoretically investigated.
These states are argued to be strongly bound, so that electron-hole
dissociation is not observed up to high electric field intensities. Trions in
the anisotropic case of monolayer phosphorene are demonstrated to especially
robust under electric fields, so that fields as high as 100 kV/cm yield no
significant effect on the trion binding energy or probability density
distribution. Polarizabilities of excitons are obtained from the parabolicity
of numerically calculated Stark shifts. For trions, a fourth order Stark shift
is observed, which enables the experimental verification of hyperpolarizability
in 2D materials, as observed in the highly excited states of the Rydberg series
of atoms and ions.
