Shubnikov–de Haas Oscillations in the Magnetoresistance of Layered Conductors in Proximity to the Topological Lifshitz Transition

Abstract

The dependence of the resistance of a layered conductor with a quasi-two-dimensional charge carrier energy spectrum on the strength and orientation of a quantizing magnetic field is studied. The case of an organic conductor with a multisheet Fermi surface consisting of a weakly warped cylinder and two adjoining planar sheets is considered. By applying an external pressure to the conductor or doping it with impurity atoms, the gap between the cylinder and the planar sheets of the Fermi surface (FS) may be reduced so that electrons start wandering on the FS, tunneling between its different parts due to magnetic breakdown. If an electron can pass through all the different sheets of the FS several times during the mean free time, its motion in the plane orthogonal to the magnetic field becomes finite. This leads to Shubnikov–de Haas oscillations with a period determined by the area enclosed by the closed breakdown orbit of an electron in momentum space. However, even at a slight tilting of the field from the normal to the layers by an angle ϑ, the equidistance is broken and at certain angles ϑk the probability of the magnetic breakdown to one of the planar FS sheets may become so low that the electron cannot complete the magnetic-breakdown orbit and its motion over the other planar sheet and the cylindrical part of the FS becomes infinite. As a result, magnetic-breakdown quantum oscillations of magnetization and all kinetic properties vanish. This vanishing repeats periodically as a function of tan ϑ with changing the tilt angle. Possibilities for experimental observation and investigation of the influence of magnetic breakdown on quantum oscillation phenomena are discussed.