Anomalous field dependence of the Hall coefficient in disordered metals

We report on a comprehensive study of the Hall coefficient, $R_H$, in disordered three-dimensional ${\mathrm{In}}_2$ ${\mathrm{O}}_{3\mathrm{-}\mathrm{x}}$ films as a function of the magnetic field strength, temperature, and degree of spatial disorder. Our main result is that, at sufficiently small fields, $R_H$ is virtually temperature, field, and disorder independent, even at the metal-insulator transition itself. On the other hand, at the limit of strong magnetic fields, $R_H$ has an explicit temperature dependence, in apparent agreement with the prediction of Al’tshuler, Aronov, and Lee. For intermediate values of fields, $R_H$ is field and temperature dependent. It is also shown that the behavior of the conductivity as a function of temperature, σ(T), at small fields, is qualitatively different than that measured at the limit of strong magnetic fields. The low- and high-field regimes seem to correlate with the respective regimes in terms of the Hall-coefficient behavior. It is suggested that the magnetotransport in the high-field limit is considerably influenced by Coulomb-correlation effects. However, in the low-field regime, where both correlations and weak-localization effects are, presumably, equally important (and where both theories are the more likely to be valid), is problematic; neither $R_H$ nor σ(T) gives any unambiguous evidence to the existence of interaction effects. This problem is discussed in light of the experimental results pertaining to the behavior of $R_H$(T) in two-dimensional ${\mathrm{In}}_2$ ${\mathrm{O}}_{3\mathrm{-}\mathrm{x}}$ films as well as in other disordered systems. It is argued that, as far as $R_H$ is concerned, the effects of weak localization and Coulomb correlations may not be additive.