Strong-Field Magnetoresistance of Impurity Conduction inn-Type Germanium

A simple theory is given of the strong-field magnetoresistance in the phonon-induced hopping region of impurity conduction in $n$-type germanium. It is shown to be convenient to consider separately the effect of a magnetic field in three cases: the weak, the moderately strong, and the extremely strong field case. In a moderately strong field the shrinking of a donor wave function and the phase difference produced by the magnetic field between two neighboring donors lead to a formula qualitatively identical with the empirical formula found experimentally by Sladek and Keyes. The magnetoresistance in an extremely strong magnetic field is also discussed, in which the wave function in the plane perpendicular to the field becomes similar to the free-electron wave function in a magnetic field.