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

Recently, a simple noninteracting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed “metal-insulator transition” in two dimensions [Y. Meir, Phys. Rev. Lett. 83, 3506 (1999)]. Here, based upon that model, a two-species percolation scaling theory is introduced and compared to the experimental data. The two species in this model are, on one hand, the “metallic” point contacts, whose critical energy lies below the Fermi energy, and on the other hand, the insulating quantum point contacts. It is shown that many features of the experiments, such as the exponential 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 critical resistance, the quenching of the metallic phase by a parallel magnetic field and the nonmonotonic dependence of the critical density on a perpendicular magnetic field, can be naturally explained by the model. Moreover, details such as the nonmonotonic dependence of the resistance on temperature or the inflection point of the resistance vs the parallel magnetic field are also a natural consequence of the theory. The calculated parallel field dependence of the critical density agrees excellently with experiments, and is used to deduce an experimental value of the confining energy in the vertical direction. It is also shown that the resistance on the metallic side can decrease with decreasing temperature by an arbitrary factor in the nondegenerate regime $(T\lesssim E_F).\mathrm{}$