I–V characteristic and magnetoresistance of homogeneous materials

A formula providing the current across a slab of homogeneous conducting material under bias and subjected to a perpendicular magnetic field, is presented in both the high and low temperature regime. The current is expressed in terms of the applied voltage, V, the magnetic field, B, temperature, T, mobility and resistivity of the material, μ and ρs at zero magnetic field and at temperature T. Furthermore, the sample dimensions enter the expression for the current. The formula in question enables obtaining the magnetoresistance of the slab in terms of the above parameters in the cases under constant bias and under constant current. Several experimental results are compared with theoretical predictions, e.g., switch from positive to negative magnetoresistance. Furthermore, it is shown that there exists a critical value for a certain dimensionless collective parameter, above which for small magnetic fields the magnetoresistance becomes negative, while for values below is positive. The quasi-linear magnetoresistance, observed in experiments at high magnetic fields, is also adequately reproduced.