Resistivity of the insulating phase approaching the 2D metal-insulator transition: the effect of spin polarization

The resistivities of the dilute, strongly-interacting 2D electron systems in the insulating phase of a silicon MOSFET are the same for unpolarized electrons in the absence of magnetic field and for electrons that are fully spin polarized by the presence of an in-plane magnetic field. In both cases the resistivity obeys Efros-Shklovskii variable range hopping $\rho(T) = \rho_0 \mbox{exp}[(T_{ES}/T)^{1/2}]$, with $T_{ES}$ and $1/\rho_0$ mapping onto each other if one applies a shift of the critical density $n_c$ reported earlier. With and withoug magnetic field, the parameters $T_{ES}$ and $1/\rho_0 = \sigma_0$ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.