The Shubnikov-de Haas effect in multiband quasi-two dimensional metals

We analyze the behavior of the longitudinal conductivity ${\sigma }_{zz}$ in a field perpendicular to the highly conducting plane of a quasi-2D {\em multiband} metal in the case of closed system and open systems where $\tau$ is fixed, $\tau$ oscillates due to intra-band scattering and $\tau$ oscillates due to inter-band scattering. In all but one case, we find that there are also mixing frequencies present – however they exhibit different qualitative behaviors, as befits their different origins, and in the case of inter-band scattering in an opensystem, may in fact be absent in the dHvA oscillations of that system.