Oscillatory magnetoconductivity in a linear chain of orbits coupled by magnetic breakdown

Abstract

A method is given for calculating the magnetoconductivity of a metal in the presence of magnetic breakdown. The method is based on a Kubo-Greenwood formula and the propagators are treated using a Pippard network model which is equivalent to a semi-classical approximation. Impurity scattering is represented simply by making the propagators attenuate. The method is applied to a linear chain network model, and it is found that when the relaxation time is very long compared with the cyclotron period the result is the same as suggested by Pippard using a 'quasi particle' picture. It is argued that this picture and a 'quantum interferometer' picture suggested by Stark are complementary. A brief discussion is given on 'zone oscillations' although no quantitative calculations have been attempted.