Metal-insulator and glass transitions in a 2D electron system in Si MOSFETs with a screened Coulomb interaction

We present a study of conductivity $\sigma$ of a 2D electron system (2DES) in Si MOSFETs with the oxide thickness $d_{ox}=7$~nm. In the low density regime of interest, the average electron-electron ($e$-$e$) separation is larger than $d_{ox}$, so that the $e$-$e$ interaction is screened by the metallic gate. The carrier density $n_s$ was changed at a high temperature $T\approx 20$~K, the 2DES was then cooled to a desired $T$ with a fixed $n_s$, and $\sigma$ was measured as a function of time $t$. At the lowest $n_s$, in the insulating regime, transport occurs via variable-range hopping. Near the critical density $n_c$ on the metallic side of the metal-insulator transition (MIT), the time-averaged $\langle\sigma(T)\rangle$ follows a power-law behavior, giving a reliable extrapolation of $\langle\sigma(n_s, T=0)\rangle$. The critical exponents are discussed and compared to the case of the MIT with long-range Coulomb interactions. The statistical analysis of the fluctuations in $\sigma(t)$ provides evidence for the glassy freezing of electrons for $n_s