On the theory of quantum oscillatons of the elastic moduli in layered conductors

In this paper we study theoretically how the local geometry of the Fermi surface (FS) of a layered conductor can affect quantum oscillations in the thermodynamic observables. We introduce a concrete model of the FS of a layered conductor. The model permits us to analyze the characteristic features of quantum oscillatory phenomena in these materials which occur due to local anomalies of the Gaussian curvature of the FS. Our analysis takes into account strong interaction among quasiparticles and we study the effect of this interaction within the framework of Fermi-liquid theory. We show that singularities in the density of states of quasiparticles (DOS) on the FS which occur at low temperatures near the peaks of its oscillations in a strong magnetic field can be significantly strengthened when the FS of the layered conductor is locally flattened. This can lead to magnetic and lattice instabilities of a special kind which are considered in the final part of the work.