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The conductivity of doped Ge below the metal-insulator transition is measured at temperatures between 4 K and 40 mK and in magnetic fields up to 7 Tesla. In zero field the resistivity exponent diverges asT-1/2. In weak fields the magnetoresistance increases asB2 and becomes exponentially large in strong fields and at low temperatures. The results can be described quantitatively in terms of variable-range hopping between localized states having a Coulomb gap in the density of states at the Fermi level. The magnetoresistance is calculated for arbitrary fields by means of a quasi-classical method. A fit to the data gives the radius of the localized states and the density of states. The sample is found to be very close to the metal-insulator transition. A small increase of the binding energy is observed in strong fields.

Variable-range hopping conduction in doped germanium at very low temperatures and high magnetic fields