  We study superradiant scattering for a charged scalar field subject to Robin
(mixed) boundary conditions on a charged BTZ black hole background. Scalar
field modes having a real frequency do not exhibit superradiant scattering,
independent of the boundary conditions applied. For scalar field modes with a
complex frequency, no superradiant scattering occurs if the black hole is
static. After exploring some regions of the parameter space, we provide
evidence for the existence of superradiantly scattered modes with complex
frequencies for a charged and rotating BTZ black hole. Most of the
superradiantly scattered modes we find satisfy Robin (mixed) boundary
conditions, but there are also superradiantly scattered modes with complex
frequencies satisfying Dirichlet and Neumann boundary conditions. We explore
the effect of the black hole and scalar field charge on the outgoing energy
flux of these superradiantly scattered modes, and also investigate their
stability.
