Symmetry Principles in the Theory of Transport Properties with Special Reference to $p$-Type Germanium

In order to solve the Boltzmann equation for low external electric and magnetic fields, taking into account details of band structure and scattering as in $p-\mathrm{G}\mathrm{e}$, the influence of crystal symmetry on scattering is discussed. The general symmetry properties of the scattering are considered and it is shown how this may facilitate the evaluation of the transport coefficients, especially those describing deviations from isotropy of the system. The method is applied to low-field magnetoconductivity and warm-carrier effects in cubic crystals like $p-\mathrm{G}\mathrm{e}$.