Relation between Low-Temperature Quantum and High-Temperature Classical Magnetotransport in a Two-Dimensional Electron Gas

Magnetotransport measurements in several GaAs/GaAlAs heterojunctions show a linear magnetoresistance at $30 \mathrm{K}<T<\mathrm{}120\mathrm{} \mathrm{K}$. At lower temperatures, where the quantum Hall effect is observed, the magnetoresistance is found to be proportional to the product of the magnetic field and the derivative of the Hall voltage with respect to the field. This can be seen as the extension of the classical linear magnetoresistance to the quantum regime. A relation between Hall voltage and magnetoresistance valid for all samples and temperatures is given.