Magnetoresistivity of Metals I. General Theory

A general theory is given for the low‐temperature magnetoresistivity of metals. This is valid for arbitrary shapes of the Fermi surface, for arbitrary elastic scattering mechanisms, and for all magnetic field strengths with the exception of the so‐called quantum limit. The derivation of the Boltzmann equation and the necessary conditions on the scattering probabilities and potentials are carefully treated. It is shown that the electrical conductivity in a magnetic field (including the Shubnikov‐de Haas effect) can be calculated exactly if the scattering of the electrons is formulated in terms of Wannier functions. The simplifications of the general case due to symmetries are discussed.