Theory of the Shubnikov de Haas effect in quasi-two-dimensional metals

The Shubnikov de Haas effect in quasi-two-dimensional normal metals is studied. The interlayer conductivity is calculated using the Kubo formula. The electron scattering on short-range impurities is considered in the self-consistent Born approximation. The result obtained is given in the analytical form, that allows an easy comparison with experimental data. It differs from the result derived using the Boltzmann transport equation. This difference is shown to be a general feature of conductivity in magnetic field. A detailed description of the field-dependent phase shift of beats and of the slow oscillations of conductivity is provided. The obtained results are applicable to strongly anisotropic organic metals and to other quasi-two-dimensional compounds.