Theory of the metal-insulator transition in two-dimensional electron systems

The metal-insulator transition in a two-dimensional disordered electron system (as the carrier concentration decreases) is considered in terms of a percolation theory. The fact that this is a strong-coupling system is substantially taken into account. In our model, the initial structure is taken to be the skeleton of an infinite cluster. Percolation paths are assumed to have regions where two phases having similar energies, namely, liquid (conducting) and solid (nonconducting) phases, can compete with each other. The ratio of these phases changes as a function of the system parameters and temperature. This behavior generates a change in the infinite cluster and results in the conductor-insulator transition. The obtained temperature dependences of resistivity agree qualitatively with experiment. A quantitative comparison of the calculated results with experimental data allows the system parameters to be estimated in each specific case. The temperature dependences of resistivity are mainly determined by the sign of the difference (and also the scatter of) in the initial energies of the phases, and they have a metallic, dielectric, or intermediate (nonmonotonic temperature dependence with a maximum) character. A separatrix can occur only in the case of a sufficiently small scatter of the phase energies.