Numerical calculations for large positive magnetoresistance ratios R(B)/R(0) in insulating materials

Numerical calculations are presented for predicting the large positive magnetoresistance ratios R(B)/R(0) which are often observed in insulating materials. The magnetic field causes shrinkage of the localized electronic wave function, resulting in less overlapping between the hopping sites and hence a relatively large increase of the resistance in the insulating material. Two specific cases are considered: (a) an insulating 3D sample that exhibits a `Mott' variable-range hopping law in its zero-field resistance and (b) an insulating 3D sample that exhibits an `Efros-Shklovskii' variable-range hopping law in its zero field resistance. The numerical calculations are tabulated. The general 3D `soft gap' case is also discussed.