Phase diagram and validity of one-parameter scaling near the two-dimensional metal-insulator transition

Abstract

We explore the scaling description for a two-dimensional metal-insulator transition (MIT) of electrons in silicon. Near the MIT, $\beta_{T}/p = (-1/p)d(\ln g)/d(\ln T)$ is universal (with $p$, a sample dependent exponent, determined separately; $g$--conductance, $T$--temperature). We obtain the characteristic temperatures $T_0$ and $T_1$ demarking respectively the quantum critical region and the regime of validity of single parameter scaling in the metallic phase, and show that $T_1$ vanishes as the transition is approached. For $T<T_1$, the scaling of the data requires a second parameter. Moreover, all of the data can be described with two-parameter scaling at all densities -- even far from the transition.