  A microscopic theory of the phonon-induced resistance oscillations in weak
perpendicular magnetic fields is presented. The calculations are based on the
consideration of interaction of two-dimensional electrons with
three-dimensional (bulk) acoustic phonons and take into account anisotropy of
the phonon spectrum in cubic crystals. The magnetoresistance is calculated for
[001]-grown GaAs quantum wells. The results are in agreement with available
experimental data. Apart from the numerical results, analytical expressions for
the oscillating part of magnetoresistance are obtained. These expressions are
valid in the region of high-order magnetophonon resonances and describe the
oscillating magnetoresistance determined by several groups of phonons polarized
along certain high-symmetry directions.
