Magnetoresistance and Hall effect due to Bragg reflection of free electrons in aluminium

The free-electron solution of the Boltzmann transport equation with electric and magnetic fields, and a constant relaxation time, may be represented as a bodily translation of the Fermi surface. However, this solution is not continuous for equivalent points at the Brillouin-zone boundaries. A solution of the Boltzmann equation satisfying the continuity conditions of Bragg reflections is constructed. The solution leads to longitudinal and transversal magnetoresistance as well as Hall effect, all varying with the magnetic field strength. The calculations were performed for aluminium with the magnetic field along one cube axis. With no adjustable parameters the theory gives semi-quantitative agreement with experimental results.