  Results are presented for the optical Hall conductivity of a Floquet
topological insulator (FTI) for an ideal closed quantum system, as well as an
open system in a nonequilibrium steady-state with a reservoir. The
steady-state, even for the open system, is strongly dependent on the
topological phase of the FTI, with certain phases showing a remarkable
near-cancellation from pockets of Berry-curvature of opposite signs, leading to
a suppressed low-frequency Hall conductivity, that also shows an anomalous
temperature dependence, by increasing as the temperature of the reservoir is
increased. Such a behavior is in complete contrast to heating, and arises
because of a strong modification of the effective system-reservoir coupling by
the laser. The Berry curvature of the Floquet modes is time-dependent, and its
frequency components are found to control the main features of the
high-frequency Hall conductivity.
