Nonlinear theory of fractional microwave-induced magnetoresistance   oscillations in a dc-driven two-dimensional electron system
  Microwave-induced nonlinear magnetoresistance in a dc-driven two-dimensional electron system is examined using a multi-photon-assisted transport scheme direct controlled by the current. It is shown that near the 2nd subharmonic of the cyclotron resonance, the frequency of the resistivity oscillation with the magnetic-field-normalized current-density is double that at the cyclotron resonance and its harmonics, in excellent agreement with recent experimental findings by Hatke {\it et al.} [Phys. Rev. Lett. {\bf 101}, 246811 (2008)]. The current-induced alternative emergence of resonant two-photon and single-photon processes is responsible for this frequency doubling. Near the third subharmonic of the cyclotron resonance, the current-induced consecutive appearance of resonant 0-/3-photon, two-photon, and single-photon processes may lead to the frequency tripling of the resistivity oscillation. 
X. L. Lei