  Recently discovered modulations of Shubnikov-de Haas oscillations in
microwave-irradiated two-dimensional electron systems are shown to arise from
electron heating induced by the radiation. The electron temperature, obtained
by balancing the energy absorption from the microwave field and the energy
dissipation to the lattice through realistic electron-phonon couplings,
exhibits resonance. The modulation of the Shubnikov de Haas oscillation and the
suppression of magnetoresistance are demonstrated together with
microwave-induced resistance oscillation, in agreement with experimental
findings.
