Hall effect near the metal-insulator transition

Hall-coefficient and dc-conductivity measurements have been made, with use of the van der Pauw geometry, on uncompensated Si:As samples on both sides of the metal-insulator transition (7.77×${10}^{18}$<N<32.8×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$, 8.55×${10}^{18}$<${\mathit{n}}_{\mathit{c}}$<8.60×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$) in the temperature range 300 to 0.5 K. Much of the data was taken in temperature sweeps between 4.2 and 0.5 K at magnetic fields between 0.5 and 15 T. The insulating samples exhibit variable-range-hopping (VRH) behavior for ${\mathit{R}}_{\mathit{H}}$(N,H,T) that is similar to the VRH behavior of σ(N,H,T) and is Mott VRH in the temperature range of these experiments. The ratio of the Hall VRH characteristic temperature ${\mathit{T}}_{0\mathit{H}}$ and the Mott characteristic temperature ${\mathit{T}}_0$ as H→0 and N→${\mathit{n}}_{\mathit{c}\mathrm{-}}$ is in good agreement with the theoretical prediction of Gruenewald et al. that (${\mathit{T}}_{0\mathit{H}}$/${\mathit{T}}_0$${)}^{1/4}$=5/8. The metallic results indicate ${\mathit{R}}_{\mathit{H}}$(n,H,T)≃${\mathit{R}}_{\mathit{H}}$(n,H)[1+${\mathit{m}}_{\mathit{H}}$(n,H)${\mathit{T}}^{1/2}$] at sufficiently low temperature, analogous to earlier results for σ(n,H,T) and suggest a coefficient of the ${\mathit{T}}^{1/2}$ term for ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$ of order ${\mathit{m}}_{\mathit{x}\mathit{y}}$∼1.5${\mathit{m}}_{\mathit{x}\mathit{x}}$. The values of ${\mathit{R}}_{\mathit{H}}^{\mathrm{-}1}$(n, H→0, T→0 K) do not show the apparent critical behavior observed for Ge:Sb, Kr:Bi, and a-Si:Pt and are essentially in agreement with the weak-localization theoretical predictions of Fukuyama and of Shapiro and Abrahams. It is speculated that the differing ‘‘critical behavior’’ of these metal-insulator systems results from a spin-orbit contribution (extraordinary contribution) to the Hall coefficient.