Negative magnetoresistance in the variable-range-hopping regime inn-type GaAs

Low-field magnetoresistance measurements for compensated, n-type three-dimensional GaAs with net donor concentration just below the metal-insulator transition show a quadratic field dependence for values of B less than 750 G. Temperature-dependent measurements in zero field show that transport is by variable-range hopping, and are consistent with the presence of a Coulomb gap which narrows close to the transition. It is found that the temperature dependence of the effective area in which the flux is enclosed is not related to the temperature dependence of the optimum hopping length. The relevant dephasing time appears not to be the hopping time. Rather, phase coherence may be lost after successive hops assisted by long-wavelength acoustic phonons or as a result of electron-electron interactions.