Galvanomagnetic phenomena in organic conductors under topological phase transition

Abstract

The magnetoresistance of layered organic conductors with a multisheet Fermi surface (FS) is studied theoretically under conditions of the Lifshitz topological transition, where the FS topology may change in response to external effects acting on the conductor, such as pressure or doping with impurity atoms. Using as an example the Fermi surface consisting of a cylinder and two planes, which are slightly corrugated along the projection of the momentum pz=pn along the normal to the layers n, we analyze the magnetic-field dependence of the resistance and the Hall field in a strong external magnetic field H, where the cyclotron frequency ωc of the conduction electrons is much higher than their collision frequency 1/τ. In the immediate vicinity of the topological transition, where the distance between the different sheets of the FS becomes small, an electron can move from one sheet of the FS to another with the probability w due to the magnetic breakdown. In this case, a quadratic increase of the electric resistance across the layers with magnetic field, which occurs in the absence of the magnetic breakdown, is replaced by a linear dependence on H for w≥γ=1/ωcτ, and then reaches saturation for (1−w)≤γ. The Hall field depends substantially on the probability of a magnetic breakdown, but in the case of ωcτ≫1, its asymptote is independent of τ for all values of w. At w = 1, the quasi-planar sheets of the Fermi surface touch the corrugated cylinders, and under further perturbation acting on the conductor, there occurs a break of a flat sheet along the line of contact. As a result, separate sections of the flat FS sheet together with the cut halves of the corrugated cylinder form a new corrugated cylinder with the sign of charge carriers reversed. This is not the only scenario of the Lifshitz topological transition. Studies of the Hall effect will allow us to obtain further important information on the nature of changes in the topological structure of the electron energy spectrum under the phase transition.