Multi-photon structures in the sub-cyclotron-frequency range in   microwave photoresistance of a two-dimensional electron system
  The frequency dependence of the peak-valley pairs occurring in the magnetoresistivity of a two-dimensional electron system under enhanced microwave irradiation, which are considered to associate with multiphoton processes, is examined in the sub-cyclotron-frequency range, based on a theoretical treatment with photon-assisted electron transitions due to impurity scattering. It is shown that with equivalent radiation power (producing the same height of the main oscillation peak), much more and stronger multi-photon structures show up at lower frequency, and when frequency increases all these structures rapidly weaken, diminish and finally disappear completely. These are in agreement with the recent experimental observation [cond-mat/0608633]. 
X.L. Lei and S.Y. Liu