Magnetoresistance effect obtained from the band structure of a crystalline solid

This paper demonstrates that the Lorentz equation combined with the equation for electron drift in an external magnetic field gives a definite value for the relaxation time of the electron motion in a crystalline solid in the aforementioned field. The main result is that the product of the relaxation time and the strength of the magnetic field remain constant and are dependent only on the structure of the energy band of the solid. Free electrons, or nearly free electrons, result in the diagonal components of the tensor for magnetoresistance tending to zero for all electron states. For the electrons in a crystal lattice, the relaxation time considered along the cross-section line in the reciprocal space of a plane normal to the magnetic field and the surface of constant energy become highly anisotropic quantities.