  In this work we present a theoretical model to study the effect of microwave
radiation on Weiss oscillations. In our proposal Weiss oscillations, produced
by an spatial periodic potential, are modulated by microwave radiation due to
an interference effect between both, space and time-dependent, potentials. The
final magnetoresistance depends mainly on the spatial period of the spatial
potential and the frequency of radiation. Depending on the values of these
parameters, we predict that Weiss oscillations can reach zero resistance
states. On the other hand, these dissipationless transport states, created just
by radiation, can be destroyed by the additional presence of a periodic
space-dependent potential. Then by tuning the spatial period or the radiation
frequency, the magnetoresistance can be strongly modified.
