Linear temperature dependence of the conductivity in Si two-dimensional electrons near the apparent metal-to-insulator transition

In a high mobility two-dimensional electron system in Si, near the critical density, n(c)=0.32x10(11) cm(-2), of the apparent metal-to-insulator transition, the conductivity displays a linear temperature (T) dependence around the Fermi temperature. When sigma(0), the extrapolated T=0 conductivity from the linear T dependence, is plotted as a function of density, two regimes with different sigma(0)(n) relations are seen, suggestive of two different phases. Interestingly, a sharp transition between these two regimes coincides with n(c), and sigma(0) of the transition is similar to e(2)/h, the quantum conductance, per square. Toward T=0, the data deviate from linear sigma(T) relation and we discuss the possible percolation type of transition in our Si sample.