Investigation of the Hall effect in impurity-hopping conduction

An attempt was made to measure the Hall effect in impurity-hopping conduction which was predicted by Holstein in 1961 but has yet to be observed. The theory was extended to a regime of higher magnetic field and lower temperature to find promising conditions for the measurement. Theoretically, it was found that the Hall conductivity approaches zero for high magnetic fields, which explained a previous negative result of Amitay and Pollak. ac Hall-effect measurements were made on single crystals of p-type germanium with a gallium concentration of 1.04×${10}^{15}$ ${\mathrm{cm}}^{\mathrm{-}3}$ and at liquid-helium temperatures where hopping was the dominant mechanism contributing to the conductivity. The Hall effect from holes in the valence band dominated the measurements for T≊4 K even though the conditions were within the hopping regime for the conductivity. When the temperature was reduced, a spurious effect due to a magnetoimpedance gradient caused by magnetic field inhomogeneity was encountered and eliminated through a novel measurement technique. At T=2.5 K, f=100 kHz, and B=4.5 kG, no Hall effect was detected, resulting in an upper bound of 1.7×${10}^{\mathrm{-}13}$ ${\Omega }^{\mathrm{-}1}$ ${\mathrm{cm}}^{\mathrm{-}1}$ on the hopping Hall conductivity which is a factor of 37 below the value obtained directly from Holstein’s theory and a factor of 6 below this work’s extension of the theory.