High-temperature quantum oscillations of the magnetoresistance in layered systems

We generalize the semiclassical theory of Shubnikov--de Haas oscillations (SHO's) for layered systems that are intermediate between three and two dimensions (e.g., semiconductor superlattices and intercalation compounds). It is shown that, in contrast to three-dimensional systems, isoenergic electron transitions between different Landau levels contribute remarkably to the oscillations. Moreover, these transitions account for a particular type of ``high-temperature'' quantum oscillations (HTO's) of the magnetoresistance. The amplitude of the HTO decays anomalously slowly (as compared to the SHO) with increasing temperature. The HTO's occur if the Fermi surface has several extreme cross sections and are related to the transitions of electrons from one extreme closed trajectory to another as a result of scattering. The period of the HTO is determined by the linear combination of areas of the extreme cross sections. For interband transitions it is smaller, and for intraband transitions it is larger, than the period of SHO. We discuss the possibility of observing HTO in layered crystals having the Fermi surface in the form of corrugated cylinder. The period of the HTO is then determined by the degree of corrugation and the shape of the oscillations changes from sawtooth to sinusoidal with increasing temperature.