Observation of a Well Defined Transition from Weak to Strong Localization in Two Dimensions

We have measured the low temperature $T\le 20\mathrm{K}$ magnetoconductance (MC) of ultrathin films that have strong spin-orbit interactions and conductances $G$ spanning the weakly $G\gg G_{00}{=e}^2/2{\pi }^2ħ$ and strongly localized $G\ll G_{00}$ regimes. For $G\gg G_{00}$, the MC is negative in agreement with weak localization theory, and for $G\ll G_{00}$, it is positive in accord with theories of electron hopping transport. The MC changes sign when $G\approx G_{00}$, independent of material and temperature. The data suggest that a well defined conductance separates the weak and strong localization regimes in two dimensions.