Indications for sharp continuous phase transitions at finite temperatures connected with the apparent metal-insulator transition in two-dimensional disordered systems

In a recent experiment, Lai et al. [Phys. Rev. B 75, 033314 (2007)] studied the apparent metal-insulator transition (MIT) of a Si quantum well structure tuning the charge carrier concentration $n$. They observed linear temperature dependences of the conductivity $\sigma(T,n)$ around the Fermi temperature and found that the corresponding $T \to 0$ extrapolation $\sigma_0(n)$ exhibits a sharp bend just at the MIT. Here, reconsidering the data published by Lai et al., it is shown that this sharp bend is related to a peculiarity of $\sigma(T=const.,n)$ clearly detectable in the whole $T$ range up to 4 K, the highest measuring temperature in that work. Since this peculiarity seems not to be smoothed out with increasing $T$ it may indicate a sharp continuous phase transition between the regions of apparent metallic and activated conduction to be present at finite temperature. Hints from the literature of such a behavior are discussed. Finally, a scaling analysis illuminates similarities to previous experiments and provides understanding of the shape of the peculiarity and of sharp peaks found in $d log_{10} \sigma / d n (n)$.