Bethe-Sommerfeld expansion of transport integrals in the presence of a magnetic field

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Abstract
The magnetic field is represented by the corresponding antisymmetric tensor and the Bethe-Sommerfeld expansion is applied directly to the transport integrals. Hereby the usual division into regions of weak and strong magnetic fields is avoided. It is assumed that a scalar relaxation time-dependent only on energy-exists, and that the isoenergetic surfaces are ellipsoids with non-parabolic dispersion. Phonon drag and quantising effects of the magnetic field are not considered. The results are expressions for the transport tensors with no restrictions on the magnitude or the direction of the magnetic field. They are applied to measurements of Nernst-Ettingshausen effect.