Two-species percolation and scaling theory of the metal-insulator transition in two dimensions

Recently, a simple noninteracting-electron model, combining local quantum t unneling via quantum point contacts and global classical percolation, has b een introduced in order to describe the observed "metal-insulator transitio n" in two dimensions [Y. Meir, Phys. Rev. Lett. 83, 3506 (1999)]. Here, bas ed upon that model, a two-species percolation scaling theory is introduced and compared to the experimental data. The two species in this model are, o n one hand, the "metallic" point contacts, whose critical energy lies below the Fermi energy, and on the other hand, the insulating quantum point cont acts. It is shown that many features of the experiments, such as the expone ntial dependence of the resistance on temperature on the metallic side, the linear dependence of the exponent on density, the e(2)/h scale of the crit ical resistance, the quenching of the metallic phase by a parallel magnetic field and the nonmonotonic dependence of the critical density on a perpend icular magnetic field. can he naturally explained by the model. Moreover, d etails such as the nonmonotonic dependence of the resistance on temperature or the inflection point of the resistance vs the parallel magnetic held ar e also a natural consequence of the theory. The calculated parallel field d ependence of the critical density agrees excellently with experiments, and is used to deduce an experimental value of the confining energy in the vert ical direction. It is also shown that the resistance on the metallic side c an decrease with decreasing temperature by an arbitrary factor in the nonde generate regime (T less than or similar to E-F).