  We demonstrate that bistability of the nuclear spin polarization in optically
pumped semiconductor quantum dots is a general phenomenon possible in dots with
a wide range of parameters. In experiment, this bistability manifests itself
via the hysteresis behavior of the electron Zeeman splitting as a function of
either pump power or external magnetic field. In addition, our theory predicts
that the nuclear polarization can strongly influence the charge dynamics in the
dot leading to bistability in the average dot charge.
