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×{}10¹⁸N32.8×{}10¹⁸ cm^-3, 8.55×{}10¹⁸{n}c8.60×{10}¹⁸$ ${cm}^{{{-}}3}$) 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 RH(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 T0H and the Mott characteristic temperature T₀ as H{→}0 and N{→}n_c- is in good agreement with the theoretical prediction of Gruenewald et al. that (T0H/T₀{)}1/4$=5/8. The metallic results indicate ${R}H(n,H,T){R}H$(n,H)[1+${m}H$(n,H)${T}1/2] at sufficiently low temperature, analogous to earlier results for σ(n,H,T) and suggest a coefficient of the{T}1/2$ term for ${{{σ}}}xy$ of order ${m}xy~1.5{m}ₓₓ$. The values of ${R}H^{{{-}}1}$(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.