Local Geometry of the Fermi Surface and Quantum Oscillations in the Linear Response of Metals

In this paper we present a theoretical analysis of the effect of anomalies of the Fermi surface (FS) curvature on oscillations in the electron density of states (DOS) in strong magnetic fields. It is shown that the oscillations could be significantly strengthened when the FS curvature turns zero in the vicinities of some extremal cross sections, and they could be weakened when the curvature takes on extremely large values or diverges there. This leads to a characteristic dependence of the oscillations magnitude on the direction of the magnetic field which is studied. The results of these general studies are employed to analyze the effects of the FS curvature anomalies on the quantum oscillations in the velocity of sound waves travelling in metals.