A low density finite temperature apparent "insulating" phase in 2D systems

We propose that the observed low density insulating'' phase of a 2D semiconductor system, with the carrier density being just below ($n < n_c$) the so-called critical density where the derivative of resistivity changes sign at low temperatures (i.e. resistivity $\rho(T)$ increases with increasing $T$ for $n > n_c$ whereas it decreases with increasing $T$ for $n < n_c$), is in fact a high-temperature’’ crossover version of the same effective metallic phase seen at higher densities ($n>n_c$). This low density ($n<n_c$) finite temperature crossover 2D effective insulating phase is characterized by $\rho (T)$ with power law temperature dependence in contrast to the truly insulating state (occurring at still lower densities) whose resistivity increases exponentially with decreasing temperature.